Dependent children can not receive SSI benefits

Perhaps I'm unclear on your question, but in general, children can not receive dependent's benefits simply because a parent receives Supplemental Security Income.

Supplemental Security Income (SSI) benefits are based on the needs of the individual and are only paid to the qualifying person. There are no spouse's, children's or survivors benefits payable.

However, if a child is disabled, that child may receive SSI benefits.

Here are relevant resources :
http://ssa-custhelp.ssa.gov/cgi-bin/ssa.cfg/php/enduser/std_adp.php?p_fa...
http://www.ssa.gov/ssi/text-child-ussi.htm

Here is a resource to see what you can do online :
http://www.ssa.gov/onlineservices/