You don't GIVE him parental rights. He already HAS parental rights just by virtue of being the biological father. You have to decide --- and do --- what's in the best interest of the child. In the long term, it's probably more important to allow your child the benefit of having a father in his/her life.
However, paying for the care of a child is part of parenthood. I don't think you'd be wrong to insist that he contribute fairly to the child's care. If he's unable to contribute at the present time, that's different from being unwilling. In my personal opinion, if he is unable to contribute at this time, I think it's unfair to penalize him --- and your child --- for that.
You'd have to check with an attorney/social worker about your local laws, but I don't think you can deny him visitation unless he's a danger to you and/or the child. Even then, there's a legal process to do so. I find it unlikely that you have legal standing anywhere to deny his rights just because you want to.
Answered Aug 31, 2012
Edited Aug 31, 2012