My cousin want to sign her rights over to me so I can take care of her babies with out going to court

Are you wanting to adopt the children? If so then it has to be done through the courts. Also where is the father of the child/children at this time?

There are no such papers. If you want to adopt the child, it has to be done through the courts. Same if you just want to assume custody or guardianship. And both parents need to be involved in this decision.

In the title you refer to what papers YOU need to sign, in the body you refer to what papers your cousin needs to sign. Which is it? Are you the mother or the prospective adoptive parent?