He has told me he doesn't want kids but expects me to look after his son on a weekend
OP as much as you may be in love, this man isn't going to fulfill your needs. He is not the only man in the world and you will not die without him, although it may feel like it if you are deeply in love.
Split with him and go completely non-contact. The only other option is to remain with him for the sake of love, growing more miserable as time goes by - and also older. Staying with him beyond child-bearing age, when you could have met someone else who would be open to you being the mother of their child, could store up so much resentment and bitterness you will find it deeply upsetting to live with.
He's told you if you can't accept his decision then you need to break up. You need to listen to him, he's told you this already and yet you are here asking for advice? Also the man is a born liar, he initially told you he wanted to start a family with you (all very convenient for him I suppose, lying meant he could get into a relationship with you) and 2 years later its "nah, I don't want that". He's a father already, he knows the score
You need to take him out of the equasion, take a deep breath decide you're not going to put a man before you and your future happiness in life, and just leave him. You're only 29 there's still time for a different and more fulfilling life but not if you continue to hang around a man who isn't on the same page as you in life