To date, no restrictions have been enacted on the purchase or possession of any .50 caliber firearms in NJ.
There have previously been attempts to enact bans of .50 cal weapons by having them reclassified as "destructive devices" under Title 2C Chapter 39 of the New Jersey Code of Criminal Justice, most recently in the 213th Legislative session of 2008 (A2116).
Early versions of the bills, being ill-conceived & poorly written, sought to ban ANY weapon greater than .50 caliber, although a revised bill excluded antiques, and those muzzleloaders approved for hunting in NJ.
Here's a copy of the last Assembly bill (with revisions):
http://www.njleg.state.nj.us/2008/Bills/A2500/2116_R3.HTM