My DP's DS1 was very antagonistic to me being around at first - he was 11 then. I very much wanted to try and sort it out - I wanted DP to talk to him, to find out what was wrong, and so we could put it right. But DP said that he thought that his DS just needed time to get used to things - he put his foot down with outright rudeness (eg refusing to sit at the same table as me) but otherwise let him protest by sulking, not talking to me, etc. His DS is not a child that finds it very easy to talk about his feelings, and DP didn't think that putting pressure on him to justify his (rather immature) behaviour would help.
But DP was right, and DS1 is alright about things now. We've had two years of not living together, but with me gradually spending increasing amounts of time round his, so that when we recently announced we were moving in, I don't think any of the DC were that surprised - and there hasn't been any further protest.
I think what I learned from this is that sometimes you do need to trust your partner to know their own DC best - what does your DP think he should do with his DS?
The other thing that I think has helped him was pressure/encouragement/mocking from his siblings. His younger brother on one ocassion embarrassed him greatly in front of me by repeating things he'd been saying. Just really babyish stuff that no 11 year old would want repeating. I'm not quite sure I would recommend this as a solution but that episode did seem to mark the end of his protest to some extent. DP also told me that he'd once moaned about me in the car and his older sister had said "Shut up [DS1]. [Purpleroses] is OK, right!" :) He really looks up to his older sister, so I'm sure that had some effect. So if your DP's DS has siblings that you get on well with, encouraging them to help him get used to you might help. Or doing things all together so that he can see that his siblings accept you.
The other thing that's helped a bit is that he realises that I am acutally a useful person to have around because I quite often take his younger siblings out and leave him to have some more quality time with his dad. So again, focussing on the kids that are happy to have you around may help, and will reassure him that he will still get time with his dad one to one.