To add to what the other moms suggested - you might want to consider some sort of activity play date (mini golf, etc.). That way, if he is not yet sure how to get the play date going, they will have a shared experience, hopefully some laughs (Strikz could be fun, Peter Piper Pizza, etc.) - and bond over those fun shared experiences. I would also suggest inviting one friend at a time, so that there is no opportunity for him to be left out.
These play dates will take a little extra work on your part in the beginning -- but he will hopefully be able to take more responsibility with each play date.
Good luck -- your son is fortunate to have a mommy who is so concerned and willing to help him.
S.