<PAGE>   1
                                                                    Exhibit 99.2

     STOCKHOLDER AGREEMENT, DATED AS OF JANUARY 25, 1999, BY AND BETWEEN BSB
      BANCORP, INC. AND CERTAIN STOCKHOLDERS OF SKANEATELES BANCORP, INC.



















                                       2


<PAGE>   2


                            SKANEATELES BANCORP, INC.

                              STOCKHOLDER AGREEMENT


        This STOCKHOLDER AGREEMENT, dated as of January 25, 1999, is entered
into by and among BSB Bancorp, Inc., a Delaware corporation ("BSB Bancorp"), and
the stockholders of Skaneateles Bancorp, Inc., a Delaware corporation
("Skaneateles"), identified on Schedule I hereto (collectively, the
"Stockholders"), who are directors, executive officers or other affiliates of
Skaneateles (for purposes of Rule 145 under the Securities Act of 1933, as
amended, and for purposes of qualifying the Merger (defined below) for
"pooling-of-interests" accounting treatment).

        WHEREAS, BSB Bancorp and Skaneateles have entered into an Agreement and
Plan of Merger, dated as of January 25, 1999 (the "Agreement"), which is
conditioned upon the execution of this Stockholder Agreement and which provides
for, among other things, the merger of Skaneateles with and into BSB Bancorp, in
a stock-for-stock transaction (the "Merger"); and

        WHEREAS, in order to induce BSB Bancorp to enter into and consummate the
Agreement, each of the Stockholders agrees to, among other things, vote in favor
of the Agreement, the Merger and the other transactions contemplated by the
Agreement in his or her capacity as a stockholder of Skaneateles;

        NOW, THEREFORE in consideration of the premises, the mutual covenants
and agreements set forth herein and other good and valuable consideration, the
sufficiency of which is hereby acknowledged, the parties hereto agree as
follows:

         1. Ownership of Skaneateles Common Stock. Each Stockholder represents
and warrants that the number of shares of Skaneateles common stock, par value
$.01 per share ("Skaneateles Common Stock"), set forth opposite such
Stockholder's name on Schedule I hereto is the total number of shares of
Skaneateles Common Stock over which such person has "beneficial ownership"
within the meaning of Rule 13d-3 under the Securities Exchange Act of 1934, as
amended, except that the provisions of Rule 13d-3(d)(1)(i) shall be considered
without any limit as to time.

         2. Agreements of the Stockholders.  Each Stockholder covenants and 
agrees that:

         (a) Such Stockholder shall, at any meeting of the holders of any or all
classes or series of Skaneateles Common Stock called for the purpose (or in
connection with any action taken by written consent), vote or cause to be voted
all shares of Skaneateles Common Stock with respect to which such Stockholder
has voting power (including the power to vote or to direct the voting of)
whether owned as of the date hereof or hereafter acquired (i) in favor of the
Agreement, the Merger and the other transactions contemplated by the Agreement
and (ii) against any plan or proposal pursuant to which Skaneateles is to be
acquired by or merged with, or pursuant to which Skaneateles proposes to sell
all or substantially all of its assets and liabilities to, any person, entity or
group (other than BSB Bancorp or any affiliate thereof) or any other action that
is inconsistent with the Agreement or the transactions contemplated thereby.
Notwithstanding the foregoing, or any other provision of this Stockholder
Agreement, BSB Bancorp shall have no agreement, arrangement or understanding
with any Stockholder as to directing the voting of any shares of Skaneateles
Common Stock to the extent it would result in BSB Bancorp, individually or with
any of its Affiliates (as defined in the next sentence) or Associates (as
defined in the next sentence) becoming the Beneficial Owner (as defined in the
next sentence) of five percent or more of the Voting Stock (as defined in the
next sentence) of Skaneateles. The terms "Affiliates," "Associates," "Beneficial
Owner," and "Voting Stock" are as defined or referenced in Article 12 of the
Skaneateles Certificate of Incorporation. In determining which, if any,
Stockholder that BSB Bancorp shall have no agreement, arrangement or
understanding with as to directing the voting of any shares of Skaneateles
Common Stock, reference shall be made to the Stockholders in order of the amount
of Skaneateles Common Stock set forth opposite such Stockholder's name on
Schedule I hereto, beginning with the Stockholder who reports the fewest number
of shares, and continuing in ascending order therefrom.


<PAGE>   3

        (b) Except as otherwise expressly permitted hereby, such Stockholder
shall not sell, pledge, transfer or otherwise dispose of his or her shares of
Skaneateles Common Stock; provided, however, that this Section 2(b) shall not
apply to a pledge existing as of January 1, 1999.

        (c) Such Stockholder shall not in his or her capacity as a stockholder
of Skaneateles directly or indirectly encourage or solicit, initiate or hold
discussions or negotiations with, or provide any information to, any person,
entity or group (other than BSB Bancorp or an affiliate thereof) concerning any
merger, sale of all or substantially all of the assets or liabilities not in the
ordinary course of business, sale of shares of capital stock or similar
transaction involving Skaneateles or otherwise inconsistent with the Agreement
or the transactions contemplated thereby. Nothing herein shall impair such
Stockholder's fiduciary obligations as a director of Skaneateles.

        (d) Stockholder shall use his or her best efforts to take or cause to be
taken all action, and to do or cause to be done all things necessary, proper or
advisable under applicable laws and regulations to consummate and make effective
the Merger contemplated by the Agreement.

        (e) Such Stockholder shall not, prior to the public release by BSB
Bancorp of an earnings report to its stockholders covering at least one month of
operations after consummation of the Merger (the "Restricted Period"), sell,
pledge (other than the replacement of a pledge existing on January 1, 1999 of
Skaneateles Common Stock), transfer or otherwise dispose of the shares of BSB
Bancorp common stock, par value $.01 per share (the "BSB Bancorp Common Stock"),
to be received by him or her for his or her shares of Skaneateles Common Stock
upon consummation of the Merger, it being agreed that BSB Bancorp shall use
commercially reasonable efforts to publish such earnings report within 45 days
after the end of the first month after the Merger becomes effective in which
there are at least 30 days of post-Merger combined operations..

        (f) Such Stockholder shall comply with all applicable federal and state
securities laws in connection with any sale of BSB Bancorp Common Stock received
in exchange for Skaneateles Common Stock in the Merger, including the trading
and volume limitations as to sales by affiliates contained in Rule 145 under the
Securities Act of 1933, as amended.

         3. Successors and Assigns. A Stockholder may sell, pledge, transfer or
otherwise dispose of his or her shares of Skaneateles Common Stock only with the
prior written consent of BSB Bancorp and if the acquirer of such Skaneateles
Common Stock agrees in writing to be bound by this Stockholder Agreement.

         4. Termination. The parties agree and intend that this Stockholder
Agreement be a valid and binding agreement enforceable against the parties
hereto and that damages and other remedies at law for the breach of this
Stockholder Agreement are inadequate. This Stockholder Agreement may be
terminated at any time prior to the consummation of the Merger by the written
consent of the parties hereto and shall be automatically terminated in the event
that the Agreement is terminated in accordance with its terms; provided,
however, that if the holders of Skaneateles Common Stock fail to approve the
Agreement or Skaneateles fails to hold a stockholders' meeting to vote on the
Agreement, then (i) Section 2(a) clause (ii) hereof shall continue in effect as
to any plan or proposal received by Skaneateles from any person, entity or group
(other than BSB Bancorp or any affiliate thereof) prior to the termination of
the Agreement or within 240 days after such termination ("Plan or Proposal") and
(ii) Section 2(b) hereof shall continue in effect to preclude a sale (other than
pursuant to normal brokers transactions on the Nasdaq Stock Market), pledge
(other than to a bona fide financial institution or recognized securities
dealer), transfer or other disposition directly or indirectly to any such
person, entity or group in connection with any such Plan or Proposal, except
upon consummation of such Plan or Proposal.

         5. Notices. Notices may be provided to BSB Bancorp and the Stockholders
in the manner specified in the Agreement, with all notices to the Stockholders
being provided to them at the addresses set forth at Schedule I.

         6. Governing Law. This Stockholder Agreement shall be governed by the 
laws of the State of Delaware, without giving effect to the principles of
conflicts of laws thereof.

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<PAGE>   4

         7.  Counterparts.  This  Stockholder  Agreement may be executed in 
one or more counterparts, all of which shall be considered one and the same and
each of which shall be deemed an original.

         8.  Headings. The Section headings contained herein are for  reference
purposes only and shall not affect in any way the meaning or interpretation of
this Stockholder Agreement.

         9. Regulatory Approval. If any provision of this Stockholder Agreement
requires the approval of any regulatory authority in order to be enforceable,
then such provision shall not be effective until such approval is obtained;
provided, however, that the foregoing shall not affect the enforceability of any
other provision of this Stockholder Agreement.

                             SIGNATURE PAGE FOLLOWS


        IN WITNESS WHEREOF, BSB Bancorp, by a duly authorized officer, and each
of the Stockholders have caused this Stockholder Agreement to be executed and
delivered as of the day and year first above written.

BSB BANCORP, INC.


By:   /s/ Alex S. DePersis
   -------------------------------------------
      Alex S DePersis
      President and Chief Executive Officer





<TABLE>
<CAPTION>
STOCKHOLDERS:

<S>                                            <C>
/s/ John P. Driscoll                            /s/ J. David Hammond
---------------------------------------        -------------------------------


/s/ Raymond C. Traver, Jr. M.D.                 /s/ Anne E. O'Connor
---------------------------------------        -------------------------------


/s/ Howard J. Miller                            /s/ David E. Blackwell
---------------------------------------        -------------------------------


/s/ Israel Berkman                              /s/ Carl W. Gerst
---------------------------------------        -------------------------------


/s/ Ann G. Higbee                               /s/ Walter D. Copeland
---------------------------------------        -------------------------------


/s/ J. Daniel Mohr                              /s/ John Bernard Henry
---------------------------------------        -------------------------------


/s/ Karen E. Lockwood                           /s/ William J. Welch
---------------------------------------        -------------------------------
</TABLE>






<PAGE>   5


                                   SCHEDULE I

                             AS OF DECEMBER 31, 1998

<TABLE>
<CAPTION>
--------------------------------------- ---------------------------------------------------------------------
                                                    Number of Shares of Skaneateles Common Stock
   Name and Address of Stockholder                               Beneficially Owned
--------------------------------------- ---------------- ----------------- ---------------- -----------------
                                        Direct               Indirect         Options/           Total
                                                                              Warrants
                                                                             Outstanding
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
<S>                                          <C>         <C>                   <C>             <C>      
John P. Driscoll                             3,017       1,024.13 (ESOP)       49,400          53,441.13
4 West Lake Street
Skaneateles, NY 13152
--------------------------------------- ---------------- ----------------- ---------------- -----------------

--------------------------------------- ---------------- ----------------- ---------------- -----------------
J. David Hammond                          4,630.8987        732 (401k)         14,250         19,723.2287
231 Beach Road, RD #4                                     110.33 (ESOP)
Auburn, NY 13021
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Karen E. Lockwood                            1,539       1,334.06 (ESOP)        6,000           8,873.06
RD#3, Route 326
Auburn, NY 13021
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
J. Daniel Mohr                             231.9845        523.89 ESOP          5,400          6,318.3166
3427 Netherstone Ct.                                     162.4421 401(k)
Baldwinsville, NY 13027
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
William J. Welch                          5,065.5326         2,501.97           9,675         17,242.5026
60 East Elizabeth Street
Skaneateles, NY 13152
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Israel Berkman                               3,434              0               3,000            6,434
101 Farmington Drive
Camillus, NY 13031
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
David E. Blackwell                        3,071.0275            0               1,500          4,571.0275
80 West Lake Street
Skaneateles, NY 13152
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Walter D. Copeland                             0            1,987.7004          3,000          4,987.7004
223 Emann Drive                                             (Revocable
Camillus, NY 13031                                        Living Trust)
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Carl W. Gerst, Jr.                           6,507              0               3,000            9,507
115 East Genesee Street
Skaneateles, NY 13152
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
John Bernard Henry, M.D.                     3,943              0               3,000            6,943
4728 Amerman Road
Skaneateles, NY 13152
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Ann G. Higbee                             6,603.4526            0               3,000          9,603.4526
Sturdy Lane
3391 East Lake Road
Skaneateles, NY 13152
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Howard J. Miller                             3,181        750 (by wife)         3,000            6,931
137 Northwood Way
Camillus, NY 13031
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Francis R. O'Connor                         10,416              0             3,000 (*)          13,416
7646 Linkside Drive
Manlius, NY 13104
--------------------------------------- ---------------- ----------------- ---------------- -----------------
--------------------------------------- ---------------- ----------------- ---------------- -----------------
Raymond C. Traver, Jr., M.D.              5,007.0104      6,075 (pension        3,000         14,868.0104
2637 East Lake Road                                           plan)
Skaneateles, NY 13152                                    393 (for child)
                                                         393 (for child)
--------------------------------------- ---------------- ----------------------------------------------------
                                                                                Total         182,859.4288
                                                                           ---------------- -----------------
</TABLE>

(*) In name of Anne O'Connor.