Not with a lawyer present, not with a notary, not for money.

Parental rights are terminated by a court and only by a court, after a proceeding, with findings, and in most circumstances only where an adoption is available to take the child.

There is no contract that does it.

You cannot write one.

If you sign a piece of paper saying you surrender your parental rights, you have written on a piece of paper.

And a purported pre-birth surrender is worse than merely unenforceable.