He first needs to be legally adjudicated as the father of the children and get his rights established. Along with those rights will also come duties and obligations. Both parents need a written order in place to establish their respective rights and obligation and to make sure those rights are protected. This is a complicated area and it is risky to try to navigate the process alone.
It is the right of the child to be supported by both parents. Even if you don't need the support now, you need to consider whether the child will need it in the future. The obligation to pay, and the right to receive, child support is separate and distinct from custody and visitation rights. You definitely need the assistance of an attorney to make sure all of the provisions are drafted correctly to protect you and the children as well as to make sure the children have what they need.
Unless you have binding Mediated Settlement Agreement or an irrevocable Rule 11 Agreement, he can change his mind up until the time the Decree is actually signed by the Judge.