AMENDED TIME-BASED RESTRICTED STOCK UNIT AWARD UNDER THE PROVISIONS OF

Exhibit 10.31 to 2008 10-K

AMENDED TIME-BASED RESTRICTED STOCK UNIT AWARD

UNDER THE PROVISIONS OF

THE CONVERGYS CORPORATION

1998 LONG TERM INCENTIVE PLAN, AS AMENDED

In 2007, pursuant to the provisions of the Convergys Corporation 1998 Long Term Incentive Plan, as amended (the “Plan”), a copy of which has been delivered to you, the Board of Directors of Convergys Corporation (the “Board”) granted you a time-based restricted stock unit award that had a Grant Date, number of Shares and Vest Date as are noted above (your “2007 restricted stock unit award”). On April 22, 2008, the Board approved certain amendments to the terms of your 2007 restricted stock unit award to document and ensure compliance with Internal Revenue Code Section 409A. The following terms, conditions and restrictions shall govern your 2007 restricted stock unit award on and after January 1, 2008.

1. Delivery of Shares. Subject to and upon the terms, conditions and restrictions set forth in this Agreement, Convergys Corporation (the “Company”) shall deliver to you the number of common shares, without par value, of Convergys Corporation (the “Shares”) indicated above 30 days following the Vest Date indicated above.

2. Forfeiture of Award. Notwithstanding the provisions of Section 1 hereof, your right to receive Shares that are the subject of this award shall be forfeited automatically and without further notice if you cease to be a member of the Board prior to the Vest Date for any reason other than your death, disability or retirement. For purposes of this Section 2 and the other provisions of this Agreement:

3. Death, Disability or Retirement. Subject to the provisions of this Section 3, if you cease to be a member of the Board both prior to the Vest Date indicated above and due to your death, disability or retirement, this award will become fully vested (i.e., vested as to all of the Shares covered by this award) as of the date you so cease to be a Board member. Notwithstanding the foregoing, if you cease to be a member of the Board due to retirement less than one year from the date this award was granted, this award will become vested only with respect to the number of Shares covered by the award that bears the same ratio as the number of days from the date of grant through the date of retirement bears to the number of days from the date of grant to the Vest Date. If this award or any portion of this award becomes vested in accordance with the provisions of this Section 3,

then, notwithstanding the provisions of Section 1 hereof, the number of Shares with respect to which this award becomes vested under the provisions of this Section 3 will be delivered 30 days following the earlier of (I) the date you separate from service from the Company and its affiliates or (II) the Vest Date indicated above. For purposes of this Section 3:

4. Rights as a Shareholder. You shall not have any rights as a shareholder of the Company with respect to any Shares that may be deliverable hereunder unless and until such Shares have been delivered to you.

5. Transferability. Your right to receive the Shares shall not be transferable nor assignable by you other than by will or by the laws of descent and distribution.

6. Compliance with Law. The Company shall make reasonable efforts to comply with all applicable federal and state securities laws; provided, however, notwithstanding any other provision of this Agreement, the Shares shall not be delivered if the delivery thereof would result in a violation of any such law. This award is intended to be compliant with the provisions of Section 409A of the Code. This award shall be construed, administered and governed in a manner that effects such intent, provided that the Company does not represent or guarantee that any particular federal or state income, estate or other tax consequences will occur because of this award and the remuneration provided hereunder.

7. Amendments. Any amendment to the Plan shall be deemed to be an amendment to this Agreement to the extent that the amendment is applicable hereto; provided, however, that no amendment shall adversely affect your rights under this Agreement without your consent.

8. Severability. In the event that one or more of the provisions of this Agreement shall be invalidated for any reason by a court of competent jurisdiction, any provision so invalidated shall be deemed to be separable from the other provisions hereof, and the remaining provisions hereof shall continue to be valid and fully enforceable.

9. Relation to Plan. This Agreement is subject to the terms and conditions of the Plan. In the event of any inconsistency between the provisions of this Agreement and the Plan, the Plan shall govern. Capitalized terms used herein without definition shall have the meanings assigned to them in the Plan. The Board acting pursuant to the Plan, as constituted from time to time, shall, except as expressly provided otherwise herein, have the right to determine any questions which arise in connection with the grant of this award.

10. Successors and Assigns. Without limiting Section 5 hereof, the provisions of this Agreement shall inure to the benefit of, and be binding upon, your successors, administrators, heirs, legal representatives and assigns, and the successors and assigns of the Company.

11. Governing Law. The interpretation, performance, and enforcement of this Agreement shall be governed by the laws of the State of Ohio, without giving effect to the principles of conflict of laws thereof.

Please indicate your acceptance of this amended award by signing below.