I just bought a car with a clean diesel motor from Indiana. The car used to be gasoline but previous owner swapped it himself with no apparent proof that it was purchased and swapped. Now its in New Jersey. Over here diesel motors do not require inspection but the VIN on title show the car to run on gas and THAT requires inspection. The odometer shows original miles and the diesel has half of that. So I am trying to figure out to fix this problem without anything coming to bite back. Any pointers?

NJ DMV is very particular. You would have to call them and if you are lucky, you will get someone that not only knows what they are talking about but is also willing to take the time to talk to you.

I am fairly sure that the car itslef will still need an inspection, just no emissions test would be done but how to prove that based on the VIN is going to be up to NJ DMV.

You will likely have to file a Vin adjustment. Not sure how hard that is in NJ but here in MO you need the Vin off the new motor, it has to be the same year or newer than the car, and for all 96 (obd2) and newer the engine had to have been available in the car from the factory.