We are Peter's and Paul's cousins.

We are Peter and Paul's cousins.

--- I think the first one says that they both may have different cousins and the second that they both have the same cousins. Although I'm not sure these are good examples.

The we in question are cousins of Peter and of Paul (who don't even necessarily have to be related - it could be opposite sides of the family). Unless context should dictate some other meaning, I think that the 's should be used with both names.
Thanks a lot for the answer.