<PAGE>

                                                                   Exhibit 10.13


                           CENTRAL CO-OPERATIVE BANK

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

                     1999 Amendment to Severance Agreement
                           with William P. Morrissey

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

     WHEREAS, Central Co-operative Bank (the "Bank") has entered into a
severance  agreement (the "Severance Agreement") with William P. Morrissey,
dated December 14, 1994; and

     WHEREAS, in connection with the acquisition of the Bank by its Holding
Company, Central Bancorp, Inc. (the "Company") the parties to the Severance
Agreement mutually desire to update its change-in-control provisions.

     NOW, THEREFORE, pursuant to Section 6 of the Severance Agreement, the
undersigned agree to amend the Severance Agreement as follows, effective upon
the date of the acquisition of the Bank by the Company.

     1.   Section 1(a) and the first clause of Section 1(b) of the Severance
Agreement shall be amended in their entirety to provide as follows:

          (a) If the Employee's employment is terminated by the Bank, without
          the Employee's prior written consent, in connection with or within
          twelve (12) months after any change in control (as herein defined) of
          the Bank or Central Bancorp, Inc. (the "Company") , the Employee shall
          be paid an amount equal to two (2) times the Employee's annual base
          salary amount at the rate in effect immediately prior to the date of
          the change in control.  In no event, however, shall such amount exceed
          the difference between (i) the product of 2.99 times the Employee's
          "base amount" as defined in Section 280G(b)(3) of the Internal Revenue
          Code of 1986, as amended (the "Code") and regulations promulgated
          thereunder, and (ii) the sum of any other parachute payments (as
          defined under Section 280G(b)(2) of the Code) that the Employee
          receives on account of the change in control.  Said sum shall be paid
          in one lump sum within ten (10) days after such termination.  The term
          "change in control" shall mean (1) the ownership, holding or power to
          vote more than 25% of the  voting stock of the Bank or the Company,
          (2) the control of the election of a majority of the Bank's or the
          Company's directors, (3) the exercise of a controlling influence over
          the management or policies of the Bank or the Company by any person or
          by persons acting as a "group" (within the meaning of Section 13(d) of
          the Securities Exchange Act of 1934), or (4) during any period of two
          consecutive years,
<PAGE>

          individuals who at the beginning of such period constitute the Board
          of Directors of the Bank or the Company (the "Company Board") (the
          "Continuing Directors") cease for any reason to constitute at least
          two-thirds thereof, provided that any individual whose election or
          nomination for election as a member of the Company Board was approved
          by a vote of at least two-thirds of the Continuing Directors then in
          office shall be considered a Continuing Director. The term "person"
          means an individual other than the Employee, or a corporation,
          partnership, trust, association, joint venture, pool, syndicate, sole
          proprietorship, unincorporated organization or any other form of
          entity not specifically listed herein.

          (b)  The Employee may voluntarily terminate his employment under this
          Agreement within twelve (12) months following a change in control of
          the Bank or the Company,

     2.   Nothing contained herein shall be held to alter, vary or affect any of
the terms, provisions, or conditions of the Severance Agreement, other than as
stated above.


     WHEREFORE, on this 8th day of January, 1999, the undersigned hereby execute
this 1999 Amendment to the Severance Agreement.

                                    CENTRAL CO-OPERATIVE BANK
Witnessed by:


/s/ Gladys N. Partamian             By   /s/ John D. Doherty
---------------------------------        ------------------------------
                                         Its President & CEO


                                    EMPLOYEE
Witnessed by:


/s/ Maya Som                        /s/ William P. Morrissey
---------------------------------   -----------------------------------
                                    William P. Morrissey
<PAGE>

                           CENTRAL CO-OPERATIVE BANK

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

                     1999 Amendment to Severance Agreement
                              with David W. Kearn

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


     WHEREAS, Central Co-operative Bank (the "Bank") has entered into a
severance  agreement ("Severance Agreement") with David W. Kearn dated December
14, 1994; and

     WHEREAS, in connection with the acquisition of the Bank by its Holding
Company, Central Bancorp, Inc. (the "Company") the parties to the Severance
Agreement mutually desire to update its change-in-control provisions.

     NOW, THEREFORE, pursuant to Section 6 of the Severance Agreement, the
undersigned agree to amend the Severance Agreement as follows, effective upon
the date of the acquisition of the Bank by the Company.

     1.   Section 1(a) and the first clause of Section 1(b) of the Severance
Agreement shall be amended in their entirety to provide as follows:

          (a) If the Employee's employment is terminated by the Bank, without
          the Employee's prior written consent, in connection with or within
          twelve (12) months after any change in control (as herein defined) of
          the Bank or Central Bancorp, Inc. (the "Company"), the Employee shall
          be paid an amount equal to two (2) times the Employee's annual base
          salary amount at the rate in effect immediately prior to the date of
          the change in control.  In no event, however, shall such amount exceed
          the difference between (i) the product of 2.99 times the Employee's
          "base amount" as defined in Section 280G(b)(3) of the Internal Revenue
          Code of 1986, as amended (the "Code") and regulations promulgated
          thereunder, and (ii) the sum of any other parachute payments (as
          defined under Section 280G(b)(2) of the Code) that the Employee
          receives on account of the change in control.  Said sum shall be paid
          in one lump sum within ten (10) days after such termination.  The term
          "change in control" shall mean (1) the ownership, holding or power to
          vote more than 25% of the voting stock of the Bank or the Company, (2)
          the control of the election of a majority of the Bank's or the
          Company's directors, (3) the exercise of a controlling influence over
          the management or policies of the Bank or the Company by any person or
          by persons acting as a "group" (within the meaning of Section 13(d) of
          the Securities Exchange Act of 1934), or (4) during any period of two
          consecutive years, individuals who at the beginning of such period
          constitute the Board of Directors of the Bank or the Company (the
          "Company Board") (the "Continuing Directors") cease
<PAGE>

          for any reason to constitute at least two-thirds thereof, provided
          that any individual whose election or nomination for election as a
          member of the Company Board was approved by a vote of at least two-
          thirds of the Continuing Directors then in office shall be considered
          a Continuing Director. The term "person" means an individual other
          than the Employee, or a corporation, partnership, trust, association,
          joint venture, pool, syndicate, sole proprietorship, unincorporated
          organization or any other form of entity not specifically listed
          herein.

          (b) The Employee may voluntarily terminate his employment under this
          Agreement within twelve (12) months following a change in control of
          the Bank or the Company,

     2.   Nothing contained herein shall be held to alter, vary or affect any of
the terms, provisions, or conditions of the Severance Agreement, other than as
stated above.


     WHEREFORE, on this 8th day of January, 1999, the undersigned hereby execute
this 1999 Amendment to the Severance Agreement.

                                    CENTRAL CO-OPERATIVE BANK
Witnessed by:


/s/ Gladys N. Partamian             By   /s/ John D. Doherty
--------------------------------         --------------------------------
                                         Its President &CEO


                                    EMPLOYEE
Witnessed by:


/s/ Maya Som                        /s/ David W. Kearn
--------------------------------    ---------------------------------------
                                    David W. Kearn
<PAGE>

                           CENTRAL CO-OPERATIVE BANK

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

                     1999 Amendment to Severance Agreement
                              with Paul S. Feeley

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

     WHEREAS, Central Co-operative Bank (the "Bank") has entered into a
severance  agreement (the "Severance Agreement") with Paul S. Feeley, dated May
14, 1998; and

     WHEREAS, in connection with the acquisition of the Bank by the Holding
Company, Central Bancorp, Inc. (the "Company"), the parties to the Severance
Agreement mutually desire to update its change-in-control provisions.

     NOW, THEREFORE, pursuant to Section 6 of the Severance Agreement, the
undersigned agree to amend the Severance Agreement as follows, effective upon
the date of the acquisition  of the Bank by the Company.

     1.   Section 1(a) and the first clause of Section 1(b) of the Severance
Agreement shall be amended in their entirety to provide as follows:

          (a) If the Employee's employment is terminated by the Bank, without
     the Employee's prior written consent, in connection with or within twelve
     (12) months after any change in control (as herein defined) of the Bank or
     Central Bancorp, Inc. (the "Company"), the Employee shall be paid an amount
     equal to two (2) times the Employee's annual base salary amount at the rate
     in effect immediately prior to the date of the change in control.  In no
     event, however, shall such amount exceed the difference between (i) the
     product of 2.99 times the Employee's "base amount" as defined in Section
     280G(b)(3) of the Internal Revenue Code of 1986, as amended (the "Code")
     and regulations promulgated thereunder, and (ii) the sum of any other
     parachute payments (as defined under Section 280G(b)(2) of the Code) that
     the Employee receives on account of the change in control.  Said sum shall
     be paid in one lump sum within ten (10) days after such termination.  The
     term "change in control" shall mean (1) the ownership, holding or power to
     vote more than 25% of the voting stock of the Bank or the Company, (2) the
     control of the election of a majority of the Bank's or the Company's
     directors, (3) the exercise of a controlling influence over the management
     or policies of the Bank or the Company by any person or by persons acting
     as a "group" (within the meaning of Section 13(d) of the Securities
     Exchange Act of 1934), or (4) during any period of two consecutive years,
     individuals who at the beginning of such period constitute the Board of
     Directors of the Bank or the Company (the "Company Board") (the "Continuing
     Directors") cease
<PAGE>

     for any reason to constitute at least two-thirds thereof, provided that any
     individual whose election or nomination for election as a member of the
     Company Board was approved by a vote of at least two-thirds of the
     Continuing Directors then in office shall be considered a Continuing
     Director. The term "person" means an individual other than the Employee, or
     a corporation, partnership, trust, association, joint venture, pool,
     syndicate, sole proprietorship, unincorporated organization or any other
     form of entity not specifically listed herein.

     (b) The Employee may voluntarily terminate his employment under this
     Agreement within twelve (12) months following a change in control of the
     Bank or the Company,

     2.   Nothing contained herein shall be held to alter, vary or affect any of
the terms, provisions, or conditions of the Severance Agreement, other than as
stated above.


     WHEREFORE, on this 8th day of January, 1999, the undersigned hereby execute
this 1999 Amendment to the  Severance Agreement.

                                       CENTRAL CO-OPERATIVE BANK
Witnessed by:


/s/ Gladys N. Partamian                By  /s/ John D. Doherty
------------------------------------       --------------------------------
                                           Its President & CEO


                                       EMPLOYEE
Witnessed by:


/s/ Maya Som                           /s/ Paul S. Feeley
------------------------------------   ------------------------------------
                                       Paul S. Feeley