I think they spawn in June.
Two Bridges (Confluence of the Pompton River and the Passaic River I think) used to be good. It has been crappy the last couple of years because of bridge work upstream...I think it is cleared up now.... I never had a problem local with law enforcement while bow fishing there, but I haven't done it there in years....things change.
Anywere you can get a shot near Pennington Park/Westside Park in Paterson has tons of carp. I would expect to have problems with Paterson PD there though. I would like to get my boat in the water there and try to catch them on a fly rod. Would need some flies that imitate floating mulberries.
Ghostbear had a post some time ago were he shot some carp at the Greenwood Lake Dam.