Dear Jeffrey,
It's difficult approaching neighbours, especially ones you have not spoken to before. I would suggest finding common ground first. ie isn't it a lovely day/horrid weather (whichever is appropriate). Engage in polite conversation.
Then slip in at the end, (so he remembers when he walks away), wether it's possible if they could sort the squeek.
Don't refer to the door as "your door", because this makes the problem theirs. Referring to "the door" will make your neighbour subconsciously realise that this is not a personal attack on them but rather that you have a problem with the door.

Complicated I know but humans are. Therefore you have not been round to their home yet! I hope this insight into the abnormal human brain is of some help!!