<PAGE>
 
                                                                   EXHIBIT 4.13b

                     SECOND AMENDMENT TO CREDIT AGREEMENT
                     ------------------------------------

     This Second Amendment to Credit Agreement (this "Second Amendment") is
                                                      ----------------     
entered into as of the 11 day of January, 1999, by and among The Wiser Oil
Company, a Delaware corporation ("Borrower"), NationsBank, N.A. (successor by
                                  --------                                   
merger to NationsBank of Texas, N.A.), as Agent ("Agent"), and NationsBank, N.A.
                                                  -----                         
(successor by merger to NationsBank of Texas, N.A.) and Bank of Montreal, as
Banks ("Banks").
        -----   

                              W I T N E S S E T H
                              -------------------

     WHEREAS, Borrower, Agent and Banks are parties to that certain Credit
Agreement dated as of December 23, 1997 as amended by that certain First
Amendment to Credit Agreement dated as of September 30, 1998 (as amended, the
"Credit Agreement") (unless otherwise defined herein, all terms used herein with
-----------------                                                               
their initial letter capitalized shall have the meaning given such terms in the
Credit Agreement); and

     WHEREAS, pursuant to the Credit Agreement, Banks have  made a certain Loan
to Borrower and provided certain other credit accommodations to Borrower; and

     WHEREAS, the Borrower has requested that certain of the Banks or their
Affiliates enter into Hedge Transactions with the Borrower and its Subsidiaries;
and

     WHEREAS, Banks and their Affiliates have required, as a condition to
entering into certain Hedge Transactions with Borrower and its Subsidiaries,
that the Credit Agreement be amended to provide that all property standing as
security for the Obligations will secure the Borrower's and its Subsidiaries"
obligations under certain Hedge Transactions on ratable basis with the Notes.

     NOW THEREFORE, for and in consideration of the mutual covenants and
agreements herein contained and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged and confessed,
Borrower, Agent and Banks hereby agree as follows:

     Section 1.  Amendments.  In reliance on the representations, warranties,
     ---------   ----------                                                  
covenants and agreements contained in this Second Amendment, the Credit
Agreement shall be amended effective January 11, 1999 (the "Effective Date") in
                                                            --------------     
the manner provided in this Section 1.
                            --------- 

     1.1  Additional Definitions.  Section 1.1 of the Credit Agreement shall be
          ----------------------                                               
amended to add the definitions of "Collateral," "Estimated Contingent Hedge
                                   ----------    --------------------------
Liability Percentage," "Estimated Contingent Hedge Transaction Amount," "Fixed
--------------------    ---------------------------------------------    -----
Hedge Liability Percentage," "Fixed Hedge Transaction Amount," "Hedge
--------------------------    ------------------------------    -----
Transaction Amount," "Hedge Transaction Percentage," "Loan Obligations," "Loan
------------------    ----------------------------    ----------------    ----
Percentage," "Second Amendment," "Secured Affiliate," "Secured Hedge
----------    ----------------    -----------------    -------------
Transaction," and "Secured Hedge Transaction Obligations,"and which shall read
                   -------------------------------------                      
in full as follows:

          "Collateral" means any and all Property of Borrower or a Subsidiary of
           ----------                                                           
     Borrower subject to any Lien securing payment or performance of the
     Obligations.

          "Estimated Contingent Hedge Liability Percentage" means, on any date,
           -----------------------------------------------                     
     the decimal, expressed as a percentage, determined by dividing (i) the
     Estimated Contingent Hedge Transaction Amount on such date by (ii) the
     Hedge Transaction Amount on such date.
<PAGE>
 
          "Estimated Contingent Hedge Transaction Amount" means, on any date,
           ---------------------------------------------                     
     with respect to Secured Hedge Transaction Obligations that are not
     absolute, fixed, liquidated liabilities of Borrower or a Subsidiary of
     Borrower on such date, the amount estimated by Agent in good faith in
     accordance with the Hedge Transaction Documents (as defined in Section
                                                                    -------
     3A.3) and its customary policies and procedures to be the amount which
     would be the Fixed Hedge Transaction Amount under the Secured Hedge
     Transactions pursuant to which such Secured Hedge Transaction Obligations
     arose if such Secured Hedge Transactions were terminated on such date.

          "Fixed Hedge Liability Percentage" means, on any date, the decimal,
           --------------------------------                                  
     expressed as a percentage, determined by dividing (i) the Fixed Hedge
     Transaction Amount on such date by (ii) the Hedge Transaction Amount on
     such date.

          "Fixed Hedge Transaction Amount" means, on any date, the amount of
           ------------------------------                                   
     Secured Hedge Transaction Obligations outstanding on such date which
     constitute absolute, fixed, liquidated liabilities of Borrower or a
     Subsidiary of Borrower and which are due and payable on such date in
     accordance with the Hedge Transaction Documents as reflected in written
     notices from the Banks or Secured Affiliates which are parties to such
     Secured Hedge Transactions addressed to Agent specifying (a) that each such
     Secured Hedge Transaction Obligation have become an absolute, fixed,
     liquidated liability of Borrower or a Subsidiary of Borrower, (b) the
     amount thereof, and (c) the calculation of such amount in detail reasonably
     acceptable to Agent.

          "Hedge Transaction Amount" means, on any date, the sum of (a) the
           ------------------------                                        
     Fixed Hedge Transaction Amount on such date, plus (b) the Estimated
     Contingent Hedge Transaction Amount on such day.

          "Hedge Transaction Percentage" means, on any date, the decimal,
           ----------------------------                                  
     expressed as a percentage, determined by dividing (a) the Hedge Transaction
     Amount on such date, by (b) the sum of (i) the aggregate outstanding
     principal balance of the Loan and all accrued but unpaid interest thereon
     on such date, plus (ii) the Hedge Transaction Amount on such date.

          "Loan Obligations" means all present and future indebtedness,
           ----------------                                            
     obligations and liabilities, and all renewals and extensions thereof, or
     any part thereof, of Borrower or any of its Subsidiaries to any Bank
     arising pursuant to this Agreement, the Notes, the Letters of Credit, or
     the other Loan Papers, and all interest accrued thereon and costs, expenses
     and attorneys fees incurred in the enforcement or collection thereof,
     regardless of whether such indebtedness obligations and liabilities are
     direct, indirect, fixed, contingent, liquidated, unliquidated, joint,
     several or joint and several.

          "Loan Percentage" means, on any day, the decimal, expressed as a
           ---------------                                                
     percentage, determined by dividing (a) the aggregate outstanding principal
     balance of the Loan and all accrued but unpaid interest thereon as of such
     date, by (b) the sum of (i) the aggregate outstanding principal balance of
     the Loan and all accrued but unpaid interest thereon on such date, plus
     (ii) the Hedge Transaction Amount on such date.

          "Second Amendment" means that certain Second Amendment to Credit
           ----------------                                               
     Agreement dated as of January 11, 1999 among Borrower, Agent and Banks.

                                       2
<PAGE>
 
          "Secured Affiliate" means any Affiliate of any Bank that has entered
           -----------------                                                  
     into a Secured Hedge Transaction with Borrower or any Subsidiary of
     Borrower.

          "Secured Hedge Transaction" means any Hedge Transaction entered into
           -------------------------                                          
     between Borrower or any of its Subsidiaries, on the one hand, and any Bank
     or any Affiliate of any Bank, on the other hand, which has been designated
     in writing as a "Secured Hedge Transaction" by Banks holding seventy-five
     percent (75%) or more of the Total Commitment.

          "Secured Hedge Transaction Obligations" means all present and future
           -------------------------------------                              
     indebtedness, obligations and liabilities, and all renewals and extensions
     thereof, or any part thereof, of Borrower or any of its Subsidiaries, to
     any Bank or any Secured Affiliate arising under or pursuant to any Secured
     Hedge Transaction, including all costs, expenses, and attorneys" fees
     incurred in the enforcement or collection thereof, regardless of whether
     such indebtedness, obligations or liabilities are direct, indirect, fixed,
     contingent, liquidated, unliquidated, joint, several or joint and several.


     1.2  Amendment to Definitions.  The definitions of "Loan Papers," and
          ------------------------                       -----------      
"Obligations" contained in Section 1.1 of the Credit Agreement shall be amended
------------                                                                   
to read in full as follows:

          "Loan Papers" means this Agreement, the First Amendment, the Second
           -----------                                                       
     Amendment, the Notes, each  Subsidiary Guaranty, all Security Documents now
     or at any time hereafter delivered pursuant to Article IIIA, and all other
                                                    ------------               
     certificates, documents or instruments delivered in connection with this
     Agreement, as the foregoing may be amended from time to time.

          "Obligations" means, collectively (a) the Loan Obligations, and (b)
           -----------                                                       
     all Secured Hedge Transaction Obligations.

     1.3  Amendment to Certain Provisions Regarding Payments.  Section 4.2 shall
          --------------------------------------------------                    
be amended to read in full as follows:

          SECTION 4.2.  General Provisions as to Payments.  (a) Each payment of
                        ---------------------------------                      
     principal of, and interest on, the Loan and all fees payable hereunder
     shall be paid not later than 12:00 noon (Dallas, Texas time) on the date
     when due, in Federal or other immediately available funds to Agent at its
     address referred to in Section 13.1.
                            ------------ 

          (b) All principal payments received by Banks in respect of the Loan
     shall be applied, first, to Advances with Interest Periods ending on the
     date of such payment, then to Base Rate Advances, then to Eurodollar
     Advances (as Borrower shall elect but in the absence of such election, in
     such order as Agent shall elect), next maturing until such principal
     payment is fully applied, with such adjustments in such order of payment as
     Agent shall specify in order that each Bank receives its ratable share of
     each such payment.

          (c) From and after the occurrence of any Event of Default, all amounts
     collected or received by any Bank in respect of the Loan Obligations, shall
     be delivered to Agent and shall be disbursed by Agent (together with all
     other amounts collected or received by Agent in respect of the Loan
     Obligations) first to the payment of all proper costs incurred by Agent in
     connection with the collection thereof (including, reasonable expenses and

                                       3
<PAGE>
 
     disbursements of Agent), second to the payment of all proper costs incurred
     by Banks in connection with the collection thereof (including reasonable
     expenses and disbursements of Banks, but only to the extent Borrower is
     obligated therefor under the Loan Papers), third to the reimbursement of
     any advances made by Banks to effect performance by Banks of any
     unperformed covenants of Borrower under any of the Loan Papers, fourth to
     any unpaid agency fees required pursuant to Section 2.10, fifth to satisfy
                                                 ------------                  
     indemnity obligations of the Borrower and its Subsidiaries arising
     hereunder and under the other Loan Papers, and sixth, to each Bank in
     accordance with its Commitment Percentage (and any amount disbursed to any
     Bank pursuant to this clause "sixth" shall be applied by such Bank to pay
     the following items in the following order:  (i) accrued but unpaid fees
     owing to such Bank pursuant to Section 2.9, (ii) accrued but unpaid
                                    -----------                         
     interest owing to such Bank, and (iii) to the principal of the Loan owing
     to such Bank).

          (d) Notwithstanding anything contained herein to the contrary, all
     amounts received by Agent which constitute proceeds ("Proceeds") of
                                                           --------     
     Collateral and which either (i) are received by Agent after the
     acceleration of the maturity of the Loan Obligations or any failure by
     Borrower to pay such Loan Obligations in full at the Termination Date, or
     (ii) result from any sale, lease, transfer or other disposition of
     Collateral which is not permitted pursuant to Section 9.5 hereof, shall be
                                                   -----------                 
     disbursed by Agent first to the payment of all proper costs incurred by
     Agent in connection with the collection thereof (including reasonable
     expenses and disbursements of Agent), and any Proceeds remaining after the
     payment of such proper costs incurred by Agent (any "Remaining Proceeds")
                                                          ------------------  
     shall be disbursed on the effective date of receipt in accordance with
     clauses (i) and (ii) below based on the Loan Percentage and the Hedge
     Transaction Percentage in effect on such date:

               (i)  an amount equal to the Loan Percentage of all Remaining
     Proceeds received on such date will be disbursed to satisfy Loan
     Obligations and applied in the manner required by clause (c) preceding; and

               (ii) an amount equal to the Hedge Transaction Percentage of such
     Remaining Proceeds (the "Hedge Allocated Amount") will be disbursed to
                              ----------------------                       
     satisfy or secure Secured Hedge Transaction Obligations in the following
     manner:

                    (A) the Fixed Hedge Liability Percentage of the Hedge
     Allocated Amount shall be disbursed to each Bank or Secured Affiliate based
     on the percentage of the Fixed Hedge Transaction Amount held by each Bank
     or Secured Affiliate on such day; and

                    (B) the Estimated Contingent Hedge Liability Percentage of
     the Hedge Allocated Amount shall be held by Agent for the ratable benefits
     of all Banks and Secured Affiliates which hold Secured Hedge Transaction
     Obligations to secure the Obligations (the "Cash Hedging Collateral").
                                                 -----------------------
     Borrower will execute or deliver and cause its Subsidiaries to execute and
     deliver such security agreements in form and substance satisfactory to
     Agent which Agent may, in its discretion, require to fully evidence and
     perfect the Liens held by it in such Cash Hedging Collateral (however, the
     failure of Borrower to execute and deliver any such security agreement
     shall not limit or impair the Liens of Agent in and to such Cash Hedging
     Collateral). Thereafter, in the event Estimated Contingent Hedge
     Transaction Amounts become Fixed Hedge Transaction Amounts, Agent shall
     disburse Cash Hedging Collateral to pay such Fixed Hedge Transaction
     Amounts. At such intervals as Agent shall determine, but not less
     frequently than monthly, Agent shall

                                       4
<PAGE>
 
     redetermine the Estimated Contingent Hedge Transaction Amount. To the
     extent the Cash Hedging Collateral exceeds the Estimated Contingent Hedge
     Transaction Amount as then redetermined, such excess shall be disbursed by
     Agent and applied to satisfy the Loan Obligations in the manner set forth
     in Section 4.2(c) above.
        --------------

     1.4  Amendment to Certain Collateral Provisions.  Sections 3A.1(a) and (b)
          ------------------------------------------                           
shall be amended to read in full as follows:

          SECTION 3A.1.  Security.  (a) In addition to the Collateral required
                         --------                                             
     by Section 2.1(b) and Section 4.2(d), the Obligations shall be secured by
        --------------     --------------                                     
     first and prior Liens (subject only to Permitted Encumbrances) covering and
     encumbering the Initial Mortgaged Properties, the Secondary Mortgaged
     Properties and such other Mineral Interests owned by Borrower and its
     Subsidiaries which are specified by Required Banks from time to time.
     Promptly following the Effective Date of the Second Amendment, and in all
     events not later than October 16, 1998 (in the case of the Initial
     Mortgaged Properties) and October 23, 1998 (in the case of the Secondary
     Mortgaged Properties), Borrower shall execute and deliver and shall cause
     each of the Subsidiary Guarantors to execute and deliver, to Agent for the
     ratable benefit of each Bank and the Secured Affiliates, mortgages, deeds
     of trust, security agreements, assignments of production and financing
     statements and such other documents, instruments, agreements, assignments,
     conveyances, amendments and other writings, including, without limitation,
     UCC-1 financing statements (each duly authorized and executed) (the
                                                                        
     "Security Documents") as Agent shall deem necessary or appropriate all in
     -------------------                                                      
     form and substance acceptable to Agent to grant, evidence and perfect first
     and prior Liens in all Initial Mortgaged Properties and Secondary Mortgaged
     Properties.

          (b) In addition to the Security Documents required by Section 3A.2(a),
                                                                --------------- 
     Borrower shall execute and deliver to Agent, for the ratable benefit of
     each Bank and the Secured Affiliates, such additional Security Documents
     granting, evidencing and perfecting the Liens required by Section 6.1(a)
                                                               --------------
     preceding with respect to such other Mineral Interests as Agent or Required
     Banks shall specify from time to time.

     1.5  Secured Hedge Transactions.  Article IIIA of the Agreement shall be
          --------------------------                                         
amended to add a new Section 3A.3 thereto which shall read in full as follows:

          SECTION 3A.3.  Secured Hedge Transactions.  In the event any Bank or
                         --------------------------                           
     any Affiliate of any Bank proposes to enter into any Hedge Transaction with
     any Borrower or any Subsidiary of Borrower and such Bank or such Affiliate
     intends that such Hedge Transaction be classified as a "Secured Hedge
     Transaction" for purposes of this Credit Agreement, the Security
     Instruments and the other Loan Papers, such Bank or Affiliate shall deliver
     notice of such intent to Agent and each other Bank which notice shall be
     accompanied by copies (in draft form) of all documentation (including all
     exhibits, schedules and confirmations) to be entered into, in final form
     and completed to the extent practical at such time, but including, in all
     events, the term of such Hedge Transaction and the notional volume of
     Hydrocarbons which will be the subject of such Hedge Transaction (the
                                                                          
     "Hedge Transaction Documents").  The Banks may, but shall have no
     ----------------------------                                     
     obligation to, designate such Hedge Transaction as a Secured Hedge
     Transaction for purposes of this Agreement and the other Loan Papers.  Any
     such designation shall be evidenced by a written instrument executed by
     Banks holding seventy five percent (75%) or more of the Total Commitment,
     and in the absence of such written designation, such Hedge Transaction
     shall not be considered a "Secured Hedge Transaction" for purposes of this
     Agreement or any of the

                                       5
<PAGE>
 
     other Loan Papers. In the event any Hedge Transaction is designated a
     Secured Hedge Transaction, the Hedge Transaction Documents related thereto
     shall be executed substantially in the form provided to Agent and the other
     Banks, and appropriately completed (but in all events, providing for the
     same term and notional volume of Hydrocarbons set forth in the drafts of
     such documents provided to the Banks), and Agent shall be provided with
     true and correct copies of such Hedge Transaction Documents promptly upon
     execution thereof. BORROWER ACKNOWLEDGES AND AGREES THAT NO BANK NOR ANY
     AFFILIATE OF ANY BANK HAS ANY OBLIGATION UNDER THIS AGREEMENT OR ANY OTHER
     LOAN PAPER TO ENTER INTO ANY HEDGE TRANSACTION OF ANY TYPE WITH BORROWER,
     REGARDLESS OF WHETHER OR NOT SUCH HEDGE TRANSACTION WOULD CONSTITUTE A
     SECURED HEDGE TRANSACTION FOR PURPOSES OF THIS AGREEMENT OR ANY OTHER LOAN
     PAPER.

     1.6  Third Party Beneficiaries.  Section 13.14 of the Agreement shall be
          -------------------------                                          
amended to read in full as follows:

          SECTION 13.14  No Third Party Beneficiaries.  It is expressly intended
                         ----------------------------                           
     that there shall be no third party beneficiaries of the covenants,
     agreements, representations or warranties herein contained other than (a)
     Secured Affiliates, (b) transferees of all or any part of any Bank"s
     interests hereunder permitted pursuant to Section 13.10, and (c)
                                               -------------         
     participants of all or any part of any Bank"s interests hereunder solely to
     the extent permitted by Section 13.10.
                             ------------- 

     Section 2.  Representations and Warranties of Borrower.  To induce Banks
     ---------   ------------------------------------------                  
and Agent to enter into this Second Amendment, Borrower hereby represents and
warrants to Banks and Agent as follows:

             2.1  Representations and Warranties in Credit Agreement.  Each
                  --------------------------------------------------       
representation and warranty of Borrower contained in the Credit Agreement and
the other Loan Papers is true and correct on the date hereof and will be true
and correct after giving effect to the amendments set forth in Section 1 hereof.
                                                               ---------        

             2.2  Absence of Defaults.  No Default or Event of Default has
                  -------------------
occurred which is continuing.

             2.3  Due Authorization; No Conflicts.  The execution, delivery and
                  -------------------------------                              
performance by Borrower of this Second Amendment and each Security Document to
be executed pursuant hereto are within Borrower"s corporate powers, have been
duly authorized by all necessary corporate action, require no action by or in
respect of, or filing with, any governmental body, agency or official and do not
violate or constitute a default under any provision of applicable law or any
Material Agreement binding upon Borrower or the Subsidiaries of Borrower or
result in the creation or imposition of any Lien upon any of the assets of
Borrower or the Subsidiaries of Borrower except Permitted Encumbrances.

             2.4  Validity, Enforceability, Binding Effect.  This Second
                  ----------------------------------------
Amendment constitutes the valid and binding obligation of Borrower enforceable
in accordance with its terms and, when executed and delivered pursuant hereto,
each Security Document delivered hereunder will constitute the valid and binding
obligation of Borrower enforceable in accordance with its terms, except as (i)
the enforceability thereof may be limited by bankruptcy, insolvency or similar
laws affecting creditor"s rights generally, and (ii) the availability of
equitable remedies may be limited by equitable principles of general
application.

     Section 3.  Miscellaneous.
     ---------   ------------- 

                                       6
<PAGE>
 
     3.1  Reaffirmation of Loan Papers.  Any and all of the terms and provisions
          ----------------------------                                          
of the Credit Agreement and the Loan Papers shall, except as amended and
modified hereby, remain in full force and effect.

     3.2  Parties in Interest.  All of the terms and provisions of this Second
          -------------------                                                 
Amendment shall bind and inure to the benefit of the parties hereto and their
respective successors and assigns.

     3.3  Legal Expenses.  Borrower hereby agrees to pay on demand all
          --------------                                              
reasonable fees and expenses of counsel to Agent incurred by Agent in connection
with the preparation, negotiation and execution of this Second Amendment and all
related documents.

     3.4  Counterparts.  This Second Amendment may be executed in counterparts,
          ------------                                                         
and all parties need not execute the same counterpart; however, no party shall
be bound by this Second Amendment until all parties have executed a counterpart.
Facsimiles shall be effective as originals.

     3.5  Complete Agreement.  THIS SECOND AMENDMENT, THE CREDIT AGREEMENT AND
          ------------------                                                  
THE OTHER LOAN PAPERS REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY
NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES.  THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.

     3.6  Headings.  The headings, captions and arrangements used in this Second
          --------                                                              
Amendment are, unless specified otherwise, for convenience only and shall not be
deemed to limit, amplify or modify the terms of this Second Amendment, nor
affect the meaning thereof.


                          [signature pages to follow]

                                       7
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have caused this Second Amendment to
be duly executed by their respective authorized officers on the date and year
first above written.

                              BORROWER:
                              -------- 

                              THE WISER OIL COMPANY,
                              a Delaware corporation


                              By:
                                 ---------------------------------------
                                    Lawrence Finn
                                    Vice President - Finance
                                    Chief Financial Officer

                              AGENT:
                              ----- 

                              NATIONSBANK, N.A., successor by merger to
                              NationsBank of Texas, N.A., as Agent


                              By:
                                 ---------------------------------------
                                    William E. Livingstone, IV
                                    Senior Vice President


                              BANKS:
                              ----- 


                              BANK OF MONTREAL


                              By:
                                 ---------------------------------------
                              Its:
                                 ---------------------------------------



                              NATIONSBANK, N.A., successor by merger to
                              NationsBank of Texas, N.A., as Agent


                              By:
                                 ---------------------------------------
                                    William E. Livingstone, IV
                                    Senior Vice President

                                       8