My son's mother has not attempted to make any contact with him for over a year, she is also not paying child support. What can I do to have her rights relinquished so my wife can adopt him?

Normally for adoption you will have to first ask her to sign the rights over, besides that, your state will have speicific rules to first can the rights be taken away, and if they can, how.

So your first stop is an attorney to start the paper work anyway.

Yes as fr chuck has said you need to hire an attorney. They are needed for any type of adoption stuff so you would need one sooner or later and sooner is generally easier to get everything done. You first try to contact your ex and see if she will voluntarily sign over her rights (if she does then it is just a matter of paperwork). If you can't contact her or she won't agree to it then you have to go to court. Either way you need to get a lawyer.