The Cnidaria include the Sea anemones, corals, jellyfish, sea pens, and hydra, but only the corals are represented in the fosil record of New Jersey. More precisely the fossil Coral of New Jersey are all members of the Class Anthozoa; the marine polypoids. More specifically they are all members of the Order Scleractina or the Stony Corals.
The Cretaceous stony corals reported from New Jersey are members of one of the following families. Wells 1956 and Vaughn & Wells 1943 provide good descriptions of the Scleractinian corals. See Thompson 1958 for a Memoir of Vaughn.