"if someone wanted to give sole custody of their unborn child to their soon to be ex-spouce how would one go about writing it up and it be legal and binding"

Is the "ex" the father of the child? If not then it would take an adoption to remove parental rights. What is happening in this situation ?

You can not "give" custody of a unborn child.

After the child is born, the parent keeping the child will file in court for sole custody and the other parent does not fight it. The non custody parent will still have rights for visitation and also obligation to pay child support.