Should I add a return vent to a pantry that doesn't have an a/c vent?
I don't think you want to rely on encouraging cold air into the room.
I have a walk-in closet that had the same problem and I solved it with a through the wall fan similar to the one below. Mount it between a room with AC and the pantry. Cold air will blow into the pantry and the space under the door will act as a return.