I truly pray that you are not offended by my comments and questions. I have to ask you, why is it so important that your son should be baptized but nothing else in your life is of importance where God is concerned? You are living in a relationship which is against Jesus’ teachings, you yourself are not willing to commit to Christ in His Church, and your partner is evidently not fully committed to his own faith since you say that he won’t choose to marry.
We get people every week call the rectory to have their kids baptized who never go to Mass, have nothing to do with anything Catholic except their parents are Catholic, nor do they commit to anything for themselves for the future. What’s the point of baptizing these little ones? This is the predicament of the pastor of the parish, what is in the best interest of the child, is there reasonable assurance that this child will be brought up in the faith? I’ve have seen my pastor refuse and accept kids for baptism and I have no right or reason to contradict his decisions.
This is my advice for you, go to your parish priest and commit to the faith fully, join RCIA and come into the Church, why would you want something for your kids that you do not want yourself? Before, during and after that, talk to your partner about your relationship and how important living in Christ is to you. Living in sin is not living in Christ; the world tells us cohabitating is acceptable, God tells us it is sinful. I would suggest both of you can benefit from RCIA; especially if he has not received all of the Sacraments, confirmation and first communion and reconciliation.
Make an appointment with the priest and lay everything out and he will help you; but be prepared to commit. If you are not ready to commit, why should he be ready to commit?
In the words of Fr. Larry Richards, “I am willing to give God everything, until He asks for something I am not ready to give Him.” Makes sense, doesn’t it?