I was wondering if parental rights of one parent could be turned over to the other parent if someone is willing to do so. How would someone go about doing this?

I see no reason to do it, all your rights are consist of visitation, custody, and having a say in the raising of the child. If you don't want to do that, then just don't do it why sign over something they can't force you to do anyway.

If you don't want to pay child support that is a obligation, not a right, and you can't sign that away normally unless the other parent has a new spouse or perhaps partner willing to adopt.

There would not be 1000's of people sitting in jail for not paying child support if they could just sign it away.