You don't really have to do anything. No court is going to order a stop on child support even if he DOES sign away his rights.
Rights are just that--parental RIGHTS. They are the rights to determine how your child is educated, what religion they are, what medical treatment they get, things like that.
Parental OBLIGATIONS (which child support is under) are something different entirely. As parents, you have the obligation to make sure your child is fed and clothed and taken care of--that's what child support is for.
Get a lawyer just in case, but even if your ex convinces a judge to let him sign away his rights, it won't stop child support.