My daughters 4 n evan though I have no one to replace her father, me and him have both decided its best if he gives up his rights. Were not married, can we still do this if she don't have a replacement?

Not in the USA... what country are you in... its hard to read what you posted. A simple search on this site will turn up a number of times this gets asked and answered every day... fact is it takes a courts intervention... and they very rarely ever do it. And of the few times they do, most appear to be out of concern for the child's own safety.

Only a court can terminate parental rights. And courts rarely do so.

It is very unlikely that any court would allow this. Even if they did, most likely he will still be held liable for child support.
Even if you don't file for support, if you or the child collects any welfare in the US, the state will go after him for support payments.