How do I get my son father to sign over his rights?

You can't.

You can ask him to, but he probably won't, especially since it won't get him out of child support.

You can also get a lawyer and go to court and ask the court to sever his parental rights... but you'd better have a very good reason to, or they probably will not.

Taking away someone's parental rights is a very serious business, and usually does not happen unless it is voluntary , or the person is a danger to their child.

I think without his permission you have got very little chance. My ex husband was violent and I still couldn't have done it.

Sorry but you don't, he will still have to support the child finacially till the child is 18 or even older if they choose to go to college.
Have to have solid concrete proof and reasons that would prove the child would be in danger to even keep him from having visitation rights.

It would help if you explained WHY. But the pat answer is you ask him.

As noted you can't FORCE him to relinquish his parental rights. Even if he does, that does not change his reponsibility to support the child financially.

Generally, the only time this happens is when you remarry and the step parent wants to adopt. If the bio parent agrees, they can relinquish their rights and the adoptive parent takes over the responsibility.

If it's so that another man can adopt your son, just ask him. However, if for any other reason, then it doesn't happen. A father can't just "sign over" his rights so that he is no longer a part of the child's life, doesn't have to pay child support or any other reason.