Whom to suggest to publisher for endorsement of my book? I've submitted the final manuscript for a book with a reputed social science publisher. My publisher wants a list of people who might be willing to provide endorsement for the book.

Whom should I suggest? In particular, is it appropriate to suggest people I've been working with, for example my supervisors? On the one hand, they would not be neutral, but on the other hand, that seems to be precisely the point of an endorsement. Should I approach them myself before suggesting them to my publisher?

I'm not sure what exactly "endorsement" means, but I believe it's about writing one of these "blurbs" that you see on the back of some books. In any case, the purpose is for marketing, not for scientific review.
As publishing has also a commercial side, publishers do want to get their costs paid (and they hope for some profit). So, they want to ensure as good as possible that someone (libraries, institutes, ..) will buy the book. For that you need your endorsements.
There is no problem in taking you supervisors for endorsement. However, I would advise you to personally ask them for their support.
Furthermore, it would be helpful if you find some other people that may to the same - have you been to conferences, spoke with people - do you built up a personal network with other peers? If so, ask them. They should be well known people in the subject you are publishing, of course. Reputation sells.