There are plenty of Park n Rides outside of Manhattan in the NJ side. See here:
Park & Ride Lots in Hudson County | Hudson TMA
But I agree with anon725 that it's better to get into Philly and take a train or bus up here. You won't be needing your car during your visit, right? So why bother with it? Plus the train or bus will take you to Penn Station or Port Authority, only a ten minute or so walk from where your son is.