I don’t know of any NJ rescues off the top of my head, but check out Pet finder and contact your local chapter of the HRS.
A couple things to keep in mind:
If you are a minor, you would not be able to legally foster. This is the same as with adoption. An adult would need to be the one to fill out all of the paperwork and assumes all responsibility. (Again, I don’t know if you are a minor or you just live at home still…)
Some rescues require a pretty large time commitment. You (or your mom if she is the legal foster) may be spending weekends traveling to local adoption events. When you foster, the goal is to get the rabbit placed for adoption, and to do this, he/she needs to be highly visible.
Additionally, people may be coming over to your house to meet the rabbit.
You might have the bunny for a week, you might have the bunny for months. It’s emotionally taxing to foster, b/c although you know it’s temporary, you can’t help but get attached.
Let us know if you have any more questions.