I helped a friend apartment hunt a few years ago with a dog in north jerz and here are complexes we found that allowed dogs at the time:

-Chatham Arms in Chatham, NJ

-Chatham on Main in Chatham, NJ

-Eagle Rock Apartments in West Orange, NJ

-Llewelyn Terrace Apartments in West Orange, NJ

-West Mill Gardens in West Orange, NJ

-Rachel Gardens Apartments in Montville, NJ