It would be best to consult an attorney who specializes in family court issues. I have heard of cases where the father offered to give up all rights to the child if he were then released from having to provide child support. However, in each case, the mother realized that having sole custody and sole financial responsibility was more than she could handle and so she declined the offer. You play the game, you pay the price. The child is the father's responsibility also.
Think about the future of your child, do you really want your child to grow up thinking you did not want to provide for him or her. One day you will have to look them in the eyes, make sure that you can. It can have an everlasting effect on your child to feel unwanted by you.