So... NO... most NJ residents cannot buy suppressors.
There are however many of you that I know own vacation homes and properties out of state, like in PA. You may actually be able to own suppressors.
Was having this discussion with my local purveyor of fine arms and evil items, @FreedomSportsLLC.
If you own a place outside of NJ, where suppressors are legal, you are likely able to purchase one with proper documentation.
The big caveat is though, you can only keep them and shoot them in PA. Obviously illegal in NJ.