my partner knows that's not his son talking
even though he knows his son is being manipulated.
No he doesn't. He doesn't know anything of the sort and neither do you. Stop assuming that a child of nine in this sort of situation doesn't know his own mind and cannot articulate how he feels.
It might suit you both to think he's being manipulated by his mother, because it's in both your interests to insist that everyone gets along swimmingly so your DP doesn't have to split his time between his son and you.
But honestly, it soundest me as though he has spoken to his child at length and does accept that this comes from him. I think he's telling you what you want to hear to keep the peace and to spare your feelings, while accepting privately that his child is feeling unsettled and needs more one to one time with him.
There could be several things going on here.
His mother has just had a baby and he may be feeling a bit pushed out at home, however unintentionally. He's exerting some control the only way he knows how.
Perhaps he just doesn't like your son much and resents being forced into a brotherly friendship with him if he finds him annoying? This sounds likely if there were no issues previously with spending time with just you and his father.
It's also possible that he is struggling to deal with feelings of jealousy having to watch his dad interact with your son, especially if your partner now lives with you and your son. If your son is all over your DP, competing for his attention and calling him Dad that would be very hard for his son to see, and deal with emotionally. I don't know if that is happening but if it is, then you can bet his son is hurting over that.
Of course I expect you to refute that any of this is happening, but this isn't a matter of truth or lie, right or wrong, it's one of perception. If it's his son's perception of what is happening then he deserves to have his feelings acknowledged and respected.
I think you need be patient and not push it. I for one am glad that your partner is putting his child's feelings first and he will tell you when the time is right to reintroduce the idea of that 'little family unit' you obviously crave.