It is not easy. You did not give us any information. Why does he want to sign away his rights? Since you were married to him and he has probably been involved with the child, why would he want to do this? There also generally needs to be a step parent adoption.
It doesn't sound like he has any case at all to sign his rights away. You cannot just get up and decide to do it. A judge would not likely grant this based on the information you provided.
