I found these comments on a web site about just what you are going to be dealing with.
If you know the manufacturer of the trailer, contact them and they can tell you where else the VIN number is stamped on the trailer. Usually one on the frame "V" on the trailer front, sometimes on the nose under the window and sometimes inside the trailer itself are all places to check.
I know it is much more difficult to pass a trailer without proper paperwork. I honestly would be concerned of theft and buying something the person sold you had not authority to sell...it happens.
Not sure if NJ actually has someone look for the hidden VIN to make sure the vehicle/trailer is not stolen...
Remember that a obviously commercially "name" manufactured trailer is not going to pass as homemade so easily.
Below are what I found that hopefully will give you some help in your registering the trailer...
Good luck... NJ has recently gotten more complicated by making you provide much more information about the trailer. For years it has been easy to swipe someone's trailer cook up some receipts and register it as homemade.
Some folks go out and bought a $200 harbor freight trailer to get the paperwork they need. Not that I suggesting you do that. Your other alternative is to register your trailer in a state requiring less stringent proof of ownership.
Also search at SurfTalk, a lot of those guys are from Jersey and have dealt with trailer registration issues.
I don't imagine that NJ is very different from CT.
Rather than trying to recover or recreate old paperwork, I found it much less trying to simply replace the ball hitch (which is excuse enough to get it inspected by the DMV as though it had been homemade), and have a fresh VIN assigned and get them to start all paperwork from scratch.
The only caveat here is that they inspect the trailer AND THE TOW VEHICLE very thoroughly, so don't try this with any sort of sub-par vehicle or the tickets will cost more than a new trailer.