<PAGE>
 
                                                                     EXHIBIT 4.2


              CERTIFICATE OF DESIGNATIONS, PREFERENCES AND RIGHTS
                   OF SERIES B CONVERTIBLE PREFERRED STOCK OF
                     CITADEL COMPUTER SYSTEMS INCORPORATED

                      (Pursuant to Section 151(g) of the
                       Delaware General Corporation Law)

    The undersigned does hereby certify:

(a)  that he is, and at all times mentioned herein was, the duly elected and
acting Chief Operating Officer and Secretary of Citadel Computer Systems
Incorporated, a Delaware corporation (the "Company");

(b)  that the Company's Certificate of Incorporation, as amended (the
"Certificate of Incorporation"), authorizes the Company's board of directors
(the "Board of Directors") to adopt resolutions fixing the voting powers,
designations, preferences, rights and qualifications, limitations or
restrictions of any series of Preferred Stock, and the Board of Directors has
delegated such authority to its executive committee (the "Executive Committee");
and

(c)  the Executive Committee adopted the following resolutions at a meeting held
on September 24, 1996:

     WHEREAS, the Certificate of Incorporation authorizes a class of stock
designated Preferred Stock (the "Preferred Stock"), comprising 1,000,000 shares,
par value $0.01 per share, provides that such Preferred Stock may be issued from
time to time in one or more series, and vests authority in the Board of
Directors of the Company to fix or alter the voting powers, designations,
preferences and relative,  participating, optional or other special rights,
rights and terms of redemption, the redemption price or prices and the
liquidation preferences of any wholly unissued series of Preferred Stock within
the limitations set forth in the Delaware General Corporation Law, and the Board
of Directors has delegated such authority to the Executive Committee;

     WHEREAS, the Company has no outstanding shares of the Company's authorized
Preferred Stock;

     WHEREAS, there remains 1,000,000 shares of the Company's authorized but
unissued Preferred Stock eligible for designation by the Company with respect to
new series thereof;

                                       1
<PAGE>
 
     WHEREAS, the Company proposes to make an offering of up to 1,620 shares of
a new series of Preferred Stock (the "Offering"); and

     WHEREAS, it is the desire of the Company to designate a series of Preferred
Stock and to fix the powers, preferences and rights, and the qualifications,
limitations or restrictions thereof in connection with the Offering;

     NOW, THEREFORE, BE IT RESOLVED, that the Company, does hereby designate
1,620 shares of authorized but unissued Preferred Stock as Series B Convertible
Preferred Stock (the "Series B Preferred Stock"), and does hereby fix the voting
powers, preferences, and relative, participating, optional, or other special
rights and qualifications, limitations, or restrictions thereof as follows:

Part 1.   General.
          ------- 

     All shares of Series B Preferred Stock will be identical with each other in
all respects.  All of the shares of Series B Preferred Stock will be of such
rank as to any other outstanding series of Preferred Stock of the Company as to
dividends and distributions upon liquidation, dissolution or winding up, as
shall be provided in the resolutions of the Board of Directors or the Executive
Committee of the Company creating such other series, subject in each case to the
conditions contained herein.

Part 2.  Dividends.
         --------- 

     The holder of each issued and outstanding share of Series B Preferred Stock
shall be entitled to receive dividends at a rate of $50.00 per share per annum,
when and as declared by the Board of Directors of the Company.  No dividends
(other than those payable solely in shares of Common Stock of the Company) shall
be paid on or declared and set apart for any Common Stock or series of Preferred
Stock that is subordinate to the Series B Preferred Stock  so long as any shares
of Series B Preferred Stock are outstanding, unless, at the same time, an
equivalent or greater dividend or distribution is declared or paid or set apart,
as the case may be, on the Series B Preferred Stock, payable on the same day as
if fully converted into Common Stock pursuant to Part 4.  At the sole option of
the Company, dividends on each share of Series B Preferred Stock may be paid in
either (a) cash out of the assets at the time legally available for such
purposes, or (b) shares of Common Stock in an amount determined by dividing (x)
the amount of the dividend payable thereon, by (y) the Conversion Price (as
defined in Part 4 hereof) in effect on the dividend declaration date.  No
dividends shall be paid on the Series B Preferred Stock at such time as such
payment would violate the laws of the State of Delaware.

                                       2
<PAGE>
 
Part 3.  Liquidation Preference   (a)  In the event of any liquidation,
         ----------------------                                        
dissolution or winding up of the Company, either voluntary or involuntary, the
holders of the Series B Preferred Stock then issued and outstanding shall be
entitled to receive out of the assets of the Company available for distribution
to its stockholders, whether from capital, surplus or earnings, prior and in
preference to any payment or distribution and setting apart for payment or
distribution of any of the net assets or surplus funds of the Company to the
holders of the Common Stock or any series of Preferred Stock with a liquidation
preference subordinate to the Series B Preferred Stock, an amount (the
"Liquidation Preference") for each share of Series B Preferred Stock then held
by them equal to $1,000 per share (the "Stated Value") plus accrued dividends.
If upon the occurrence of such event, the assets and funds thus distributed
among the holders of the Series B Preferred Stock shall be insufficient to
permit the payment to such holders of the full Liquidation Preference, then the
entire assets and funds of the Company legally available for distribution shall
be distributed among the holders of the Series B Preferred Stock and the holders
of any other series of Preferred Stock with a liquidation preference equal to
that of the Series B Preferred Stock, in proportion to the shares of Series B
Preferred Stock or other such series of Preferred Stock then held by them.

     (b) If the assets and funds of the Company available for distribution to
the Company's stockholders exceed the aggregate Liquidation Preferences payable
to the holders of Series B Preferred Stock pursuant to paragraph 3(a) above,
then after the payments required by paragraph 3(a) shall have been made or
irrevocably set apart for payment, such assets or funds shall be distributed
among the holders of Common Stock and subordinate Preferred Stock.

     (c) (i) A consolidation or merger (within the meaning of Section 368(a) of
the Internal Revenue Code of 1986, as amended) of the Company with or into one
or more other corporations or other business organizations, (ii) the sale, lease
or transfer of all or substantially all of the assets of the Company, or (iii)
any other form of corporate reorganization in which outstanding shares of the
Company are exchanged for or converted into cash, securities of another
corporation or business organization or other property, which in any such case
shall not in fact result in a liquidation (in whole or in part) of the Company
and the distribution of its assets to its stockholders shall not be deemed or
treated as a liquidation, dissolution or winding up of the Company within the
meaning of Part 3.

Part 4.  Conversion.  The holders of Series B Preferred Stock will have the
         ----------                                                        
following conversion rights:

     (a) Right to Convert.  Each share of Series B Preferred Stock shall be
         ----------------                                                  
convertible, 

                                       3
<PAGE>
 
on and after the Conversion Dates and at the Conversion Ratio set forth below,
into fully paid and non-assessable shares of Common Stock.

     (b) Method of Conversion.  Subject to paragraph (c) below, each holder of
         --------------------                                                 
Series B Preferred Stock who desires to convert the same into shares of Common
Stock shall provide notice to the Company by the execution and delivery to it of
a Notice of Conversion in substantially the form attached as Annex A hereto.
Notice may be given by telecopy to the Company at 512.520.9293.  The date on
which a Notice of Conversion is received by the Company shall be a "Notice
Date".  The Company shall use its reasonable best efforts to issue and deliver
within five business days after receipt of the Notice of Conversion and the
certificate or certificates for the shares of Series B Preferred Stock, with
proper endorsement if necessary, from the holder electing conversion, a
certificate or certificates representing the number of shares of Common Stock to
which the holder shall be entitled to upon the conversion.

     (c) Conversion Date.  The Series B Preferred Stock shall become convertible
         ---------------   
into shares of Common Stock at any time commencing forty (40) days after the
closing date for the original issuance of the Series B Preferred Stock (the
"Conversion Date").

     (d) Conversion Ratio.  In addition to such shares of Common Stock as may be
         ----------------                                                       
issued upon the election of the Company pursuant to Part 2 above as dividends,
each share of Series B Preferred Stock shall be convertible into the number of
shares of Common Stock according to the following formula:

                                   N x 1,000
                            ----------------------
                               Conversion Price
where:

N = the number of shares of Series B Preferred Stock for which conversion is
elected.

Conversion Price = the product of (x) the average closing bid price as reported
on the Nasdaq system (or on such other national securities exchange or automated
quotation system on which the Common Stock is then primarily traded) of the
Common Stock for the five consecutive trading days immediately preceding the
Notice Date and (y) .83.

     (e) Automatic Conversion.  Each share of Series B Preferred Stock
         -------------------- 
outstanding on September 24, 1998 automatically shall be converted into Common
Stock on such date at the Conversion Ratio then in effect, and September 24,
1998 shall be deemed to be the Notice Date with respect to such conversion;
provided however, if September 24, 1998 is not a day on which the Nasdaq system
is open for trading or quotation, the deemed Notice 

                                       4
<PAGE>
 
Date shall be the next succeeding day on which the Nasdaq system is open for
trading or quotation.

     (f)  Fractional Shares.  No fractional share will be issued upon the
          -----------------                                              
conversion of any shares of Series B Preferred Stock.  All shares of Common
Stock (including fractions thereof) issuable on conversion of Series B Preferred
Stock by a holder thereof shall be aggregated for purposes of determining
whether the conversion would result in the issuance of any fractional share.
If, after the aggregation, the conversion would result in the issuance of a
fractional share, the Company shall, in lieu of issuing any fractional share,
round up or down any fractional share to the nearest whole share of Common
Stock.

     (g)  Adjustment to Conversion Price.
          ------------------------------ 

          (i) If, prior to the conversion of all shares of Series B Preferred
Stock, the number of shares of Common Stock or Series B Preferred Stock is
increased by a stock split, stock dividend, or similar event, or if the number
of shares of Common Stock or Series B Preferred Stock is decreased by a
combination, reclassification, reverse stock split, or similar event, the Board
of Directors of the Company shall make an equitable adjustment in the Conversion
Ratio, if necessary, to reflect such event in order to preserve substantially
the initial Conversion Ratio.  The Company will send to each holder of Series B
Preferred Stock written notice of each change in the Conversion Ratio.

          (ii) If, prior to conversion of all shares of Series B Preferred
Stock, there shall be any merger, consolidation, exchange of shares,
recapitalization, reorganization or similar event, as a result of which shares
of Common Stock will be ch anged into the same or a different number of shares
of the same or different class or classes of stock or other securities of the
Company or another entity, then holders of Series B Preferred Stock will
thereafter have the right to purchase and receive upon conversion of shares of
Series B Preferred Stock, on the basis and on the terms and conditions specified
herein, and in lieu of shares of Common Stock immediately theretofore issuable
upon conversion, such shares of stock or securities as may be issued or payable
with respect to or in exchange for the number of shares of Common Stock
immediately theretofore purchasable and receivable upon conversion of shares of
Series B Preferred Stock had such event not taken place.  In any case subject
hereto, appropriate provision shall be made with respect to the rights and
interests of the holders of Series B Preferred Stock to the end that the
provisions hereof (including without limitation provisions for adjustment of the
Conversion Price and the number or type of shares issuable upon conversion of
the Series B Preferred Stock) shall thereafter be applicable, as nearly as may
be practicable in relation to any shares of stock or securities thereafter
deliverable upon the exercise hereof.  The Company shall not effect any
transaction described in this subsection (ii) unless the successor or acquiring
entity (if not the Company) assumes by written instrument the obligation to
deliver to the holders of 

                                       5
<PAGE>
 
Series B Preferred Stock shares of stock or securities, as in accordance with
the foregoing, the holders of the Series B Preferred Stock may be entitled to
purchase upon conversion.

     (h) Reservation of Stock Issuable Upon Conversion.  The Company shall at
         ---------------------------------------------      
all times reserve and keep available out of its authorized but unissued shares
of Common Stock, solely for the purpose of effecting the conversion of the
shares of Series B Preferred Stock, such number of shares of Common Stock as
shall from time to time be sufficient to effect the conversion of all then
outstanding shares of Series B Preferred Stock. If at any time the number of
authorized but unissued shares of Common Stock shall not be sufficient to effect
the conversion of all then outstanding shares of Series B Preferred Stock, the
Company will take such corporate action as may be necessary to increase its
authorized but unissued shares of Common Stock to such number of shares as shall
be sufficient for such purposes.

     (i)  Status of Converted Stock.  Upon the Company receiving a Notice of
          -------------------------                                         
Conversion for any shares of Series B Preferred Stock pursuant to this section,
the shares covered by such Notice of Conversion shall no longer be deemed
outstanding and all rights with respect to such shares shall cease and be
canceled and such shares shall be returned to the status of authorized  but
unissued Preferred Stock of no designated class or series and shall not be
issuable by the Company as Series B Preferred Stock.

Part 5.  Voting Rights.
         ------------- 

     Except as otherwise expressly required by the Delaware General Corporation
Law or as to any repeal, modification, or amendment to this Certificate of
Designation, which repeal, modification, or amendment shall require the
affirmative vote of the holders of at least a majority of the shares of Series B
Preferred Stock outstanding, voting separately as a class, the holders of Series
B Preferred Stock shall have no voting power whatsoever, and no holder of Series
B Preferred Stock shall vote or otherwise participate in any proceeding in which
actions shall be taken by the Company or the stockholders thereof, or be
entitled to notification of any meeting of the Board of Directors or the
stockholders.

Part 6.  Replacement.
         ----------- 

     Upon receipt of evidence reasonably satisfactory to the Company (an
affidavit of the registered holder with indemnification provisions will be
satisfactory) of the ownership and the loss, theft, destruction or mutilation of
any certificate evidencing shares of Series B Preferred Stock, and in the case
of any such loss, theft or destruction, upon receipt of indemnity reasonably
satisfactory to the Company or, in the case of any mutilation, upon surrender of
such certificate, the Company will (at the holder's expense) execute and deliver
in lieu of such certificate a new certificate of like kind representing the
number of 

                                       6
<PAGE>
 
shares of Series B Preferred Stock represented by such lost, stolen, destroyed
or mutilated certificate, and dividends will accrue on the shares of Series B
Preferred Stock represented by such new certificate from the date to which
dividends have been fully paid on such lost, stolen, destroyed or mutilated
certificate.

     FURTHER RESOLVED, that the statements contained in the foregoing
resolutions creating and designating the Series B Preferred Stock and fixing the
number, powers, preferences and relative, optional, participating and other
special rights and the qualifications, limitations, restrictions, and other
distinguishing characteristics thereof shall, upon the effective date of such
series, be deemed to be included in the Certificate of Incorporation of the
Company pursuant to Sections 104 and 151 of the Delaware General Corporation
Law.

     The undersigned further certifies that the authorized number of shares of
Preferred Stock is 1,000,000 and that the number of shares of this series of
Preferred Stock, the Series B Convertible Preferred Stock, none of which has
been issued, is 1,620.


     IN WITNESS WHEREOF, Citadel Computer Systems Incorporated has caused this
Certificate to be executed by its duly authorized representative as of September
24, 1996.


                                CITADEL COMPUTER SYSTEMS INCORPORATED
            
            
                                By:  
                                    -------------------------------------------
                                     Steven B. Solomon, Chief Operating Officer

                                       7
<PAGE>
 
                             NOTICE OF CONVERSION

 (To be Executed by the Registered Holder to Convert Series B Preferred Stock)

The undersigned hereby irrevocably elects to convert $____________ or
____________ shares of Series B Preferred Stock into shares of Common Stock of
Citadel Computer Systems Incorporated (the "Company") according to the
conditions hereof, as of the date written below.  The undersigned represents and
warrants that (i) all of the requirements of Regulation S promulgated under the
Securities Act of 1933, as amended (the "Securities Act"), applicable to the
undersigned have been complied with by the undersigned and (ii) the undersigned
has not engaged in any transaction or series of transactions that is a part of
or a plan or scheme to evade the registration requirements of the Securities
Act.


                                   -----------------------------------------
                                   Date of Conversion*

 
                                   -----------------------------------------
                                   Applicable Conversion Price

 
                                   -----------------------------------------
                                   Dollar amount or Shares

 
                                   -----------------------------------------
                                   Signature

                                   Name and Address:

 
                                   -----------------------------------------

 

                                   -----------------------------------------
 


                                   -----------------------------------------

*The original certificate representing shares of Series B Preferred Stock and
this Notice of Conversion must be received by the Company by the fifth business
day following the Date of Conversion.

                                       8