Not soBoth you and the seller can take a ride over the border into PA and make the deal privately if you want to be completely legal about it.
According to the BATF:
If you reside in New Jersey, any transfer outside of New Jersey is not legal unless it complies with NJ law.B2) From whom may an unlicensed person acquire a firearm under the GCA? [Back]
A person may only acquire a firearm within the person’s own State, except that he or she may purchase or otherwise acquire a rifle or shotgun, in person, at a licensee's premises in any State, provided the sale complies with State laws applicable in the State of sale and the State where the purchaser resides. A person may borrow or rent a firearm in any State for temporary use for lawful sporting purposes.
[18 U.S.C. 922(a)(3) and (5), 922(b)(3), 27 CFR 478.29 and 478.30]