This is the AMA website
Academy of Model Aeronautics - AMA Charter Club Search. You can put in your zip code and it will give you a list of flying fields within a 25 mile radius. I checked quick and it looked like there were some in your area. I just believe you have to sign up for a membership for $75.00 to use the fields. These are the first 3 that popped up.
442-480 Dunhams Corner Rd, East Brunswick, NJ 08816
300 Old Georges Rd, North Brunswick Township, NJ 08902
386-400 Grove Ave, Metuchen, NJ 08840
I also live in NJ, Red Bank area, and so far haven't had any issues with the local police or park rangers. I retired as a police officer last year. In my 25 years I've attended numerous legal update courses and have never once heard of any type of NJ statute or law regarding the use of a drone. You could always contact the county and ask if there are any resolutions that prohibit the use of UAV's in the county parks. Absent that, as long as you're following the FAA guidlines, being safe and not flying over anyone in the park I don't see the issue. Maybe, if there is no county resolution or municipal ordinance prohibiting their use, print out a copy of the FAA guidelines and speak with the ranger (in a non argumentative way) and showthem to him. If you get nowhere with him, move on to his supervisor. Hope this helps, let me know how you make out.