You're in luck, PA is a kind state. They do issue non-resident liscenses, and it issues them on a shall-issue basis. That means that if they can't give a good reason for you not to have one, they must give you a liscense.

PA does not have a reciprocity agreement with NJ, though, so don't try to use the PA liscense to carry in NJ.

Packing.org -> your friend.