Backpack camping is not permitted in any New Jersey Park except for those listed below.
In the Pinelands, the 49.5 mile long Batona (Back TO Nature) Trail has designated campsites in Wharton State Forest, Brendan Byrne (formerly Lebanon) State Forest and Bass River State Forest. Permits are required. Contact the parks for specifics. Try the Outdoor Club of South Jersey.
The NYNJTC Kittatinny Trails Map and North Jersey Trails Map show tent sites and a shelter along the Appalachian Trail. A number of connecting trails shown on these maps can be combined for loop hikes. See the website of the Appalachian Trail Conservancy for more information.