NJ allows private sales between non-FFL individuals provided both people have an FID and matching NJ Driver's License, and you both fill out an NJ COE (can download the form off NJSP website).
You can also sell a handgun to an NJ resident provided has a Permit to Purchase a Pistol, and both people have an NJ Driver's license and FID, and the seller mails/gives all four copies of the Pistol Permit forms to the proper places. You don't need an NJ COE form for a handgun sale.
You CAN NOT mail/ship a gun to a fellow NJ resident, as all gun sales in NJ must be face to face. But of course you can mail to an NJ FFL.