Child SSI

This is possible, depending on the circumstances.

If you wish to become the representative payee, you should contact the SSA office nearest you to apply to be a payee. You must then submit an application, form SSA-11 (Request to be selected as payee) and documents to prove your identity. You will need to provide your social security number or if you represent an organization, the organization’s employer identification number. SSA requires you to complete the payee application in a face-to-face interview (with certain exceptions).

http://www.ssa.gov/payee/faqrep.htm

http://www.ssa.gov/online/ssa-11.pdf

I found this excerpt regarding selection of representative payee. It's specific to the state of Massachusetts, but should provide useful guidelines :

Do not routinely appoint Department of Children and Families (DCF) as payee solely because the child is placed in its care. Our primary concern must be that the payee we choose will serve the best interests of the beneficiary. Do not assume that a parent who is the current payee is no longer qualified solely because the child is in foster care. Consider why the child was placed in foster care and whether there are family members who show a strong concern when determining who will be the best payee. When you take the representative payee application, ask DCF to disclose all known information about the existence of parents and relatives who show concern. Follow the policies contained in GN 00502.105 and GN 00502.159 to develop and select the proper payee. In situations where the individual already has a representative payee, contact the current payee and develop according to GN 00504.100 .

If you decide to select the parent as payee in order to maintain the parent/child relationship but have some reservations about the decision, use the follow-up procedure in GN 00502.183 to diary the case and ensure benefits are being properly used.

https://secure.ssa.gov/poms.nsf/lnx/0200502159BOS