<PAGE>

                                                                    Exhibit 4(j)
                      AMENDMENT NO. 2 TO RIGHTS AGREEMENT
                      -----------------------------------

     Amendment No. 2, dated as of July 30, 1999 (this "Amendment"), between
United Water Resources Inc., a New Jersey Corporation (the "Company"), and
ChaseMellon Shareholder Services, LLC (the "Rights Agent"), as successor to the
trust business of First Interstate Bank, Ltd., to the Rights Agreement, dated as
of July 12, 1989 (the "Rights Agreement"), between the Company and the Rights
Agent.

     WHEREAS, the Company and the Rights Agent have entered into the Rights
Agreement;

     WHEREAS, pursuant to Section 27 of the Rights Agreement, the Board of
Directors deems it in the best interests of the Company and its shareholders,
necessary and desirable, and consistent with and for the purpose of fulfilling
the objectives of the Company's Board of Directors in authorizing the execution
of the Rights Agreement, to amend the Rights Agreement as set forth below.

     NOW THEREFORE, in consideration of the premises and the mutual promises set
forth herein and in the Rights Agreement, the parties hereto agree as follows:

     Section 1.   Section 2 of the Rights Agreement is hereby amended to read in
its entirety as follows:

     "Appointment of Rights Agent.  The Company hereby appoints the Rights Agent
     ----------------------------
to act as agent for the Company in accordance with the terms and conditions
hereof, and the Rights Agent hereby accepts such appointment.  The Company may
from time to time appoint such co-rights agents as it may deem necessary or
desirable."

     Section 2.   Section 7(a) of the Rights Agreement is hereby amended by
amending clause (i) thereof to read in its entirety as follows:
     "(i) The Close of Business on April 22, 2006 (the "Final Expiration
Date"),."
     Section 3.   Section 20(c) of the Rights Agreement is hereby amended by
adding the following sentence as the second sentence:

     "Anything to the contrary notwithstanding, in no event shall the Rights
Agent be liable for special, punitive, indirect, consequential or incidental
loss or damage of any kind whatsoever (including but not limited to lost
profits), even if the Rights Agent has been advised of the likelihood of such
loss or damage."
<PAGE>

     Section 4.   Section 23 of the Rights Agreement is hereby amended by (i)
deleting subsection (c) thereof in its entirety, and (ii) amending subsection
(a) thereof to read in its entirety as follows:

     "(a) The Rights may be redeemed by action of the Board of Directors
     pursuant to subsection (b) of this Section 23 and shall not be redeemed in
     any other manner."

     Section 5.   Section 26 of the Rights Agreement is hereby amended to delete
the reference to First Interstate Bank of California and its address on the
seventeenth through the twenty-second lines thereof and to insert in lieu
thereof the following:

          ChaseMellon Shareholder Services, LLC
          85 Challenger Road
          Ridgefield, New Jersey 07660

     Section 6.   Except as expressly set forth herein, this Amendment shall not
by implication or otherwise alter, modify, amend or in any way affect any of the
terms, conditions, covenants or agreements contained in the Rights Agreement,
all of which are ratified and affirmed in all respects and shall continue in
full force and effect.

     Section 7.   This Amendment shall be deemed to be a contract made under the
laws of the State of New Jersey and for all purposes shall be governed by and
construed in accordance with the laws of such State applicable to contracts to
be made and performed entirely within such state.

     Section 8.   This Amendment may be executed in counterparts and each of
such counterparts shall for all purposes be deemed to be an original, and all
such counterpart shall together constitute but one and the same instrument.
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to the
Rights Agreement to be duly executed and attested, all as of the date first
above written.

                                        UNITED WATER RESOURCES, INC.



                                        By:____________________________
                                        Name:
                                        Title:


Attest:


By:__________________________
  Title:



                                        CHASEMELLON SHAREHOLDER
                                        SERVICES, LLC



                                        By:___________________________
                                        Name:
                                        Title:


Attest:



By:__________________________
  Title: