Jeff,
That's a tough one. I grew up in South Jersey, and my opinion is that, like most everything in NJ, it's very difficult. I've lived in VA here for the past 11 years, and it's a bit easier and I'll get getting back into it next spring and summer. But, apparently you can do it for carp and maybe other species, and here's the link from the NJ Fish and Game site:
http://www.state.nj.us/dep/fgw/fish_carp.htm
It's just an article, so I'd call them if you want more information just to be completely legal. Down here in VA we bowfish for skates and rays off of Assateauge and Chincoteauge Islands. I'd imagine you can bowfish in the salt marshes up there. Good luck and Merry Xmas!