My kids dad wants to give up his parental rights. What paperwork do I need to give?

First make sure that he isn't assuming he will get out of child support simply because his rights are terminated.
Step two reasons he wants his rights terminated?
Step three would the Judge even go for it?

He needs to file a motion with family court to give up his rights,
Do you have a new partner who wants to adopt?

Mnay judges will not even allow them to give up their rights, unless there is a new husband or partner to adopt.
Also even if he does get the judge to allow him to give up his rights, he still has to pay his child support, that is his obligations, and does not end just because he gives up his rights ( unless there is a new partner to adopt)

I don't know if there is any such "paperwork." Usually a parent only "gives up" his/her rights to pave the way for an adoption. Otherwise giving up rights does not excuse one from paying child support and one really has nothing to gain by giving up his/her rights.