Few dinosaurs have been discovered in North Carolina, but this state is rich in other kinds of prehistoric life, as listed below. (See an interactive map of dinosaurs and prehistoric animals in the United States.)
Not quite a dinosaur, and not quite a prehistoric crocodile (despite the "suchus" in its name), Postosuchus was a splay-legged, half-ton archosaur that ranged widely across North America during the late Triassic period. A new Postosuchus species, Postosuchus alisonae, was discovered in North Carolina in 1992. More about Postosuchus
The scattered remains of Eocetus, the "dawn whale," were discovered in North Carolina in the late 1990's. This early Eocene whale, which lived about 44 million years ago, possessed rudimentary arms and legs, a snapshot of the early stages of whale evolution before these mammals had adapted to a fully aquatic existence.
It's the official state dinosaur of Missouri, but fossils of Hypsibema have been discovered in North Carolina as well. Unfortunately, this hadrosaur (duck-billed dinosaur) is what paleontologists call a nomen dubium--it was a probably an individual or species of an already-named dinosaur, and thus doesn't deserve its own genus.
North Carolina boasts some of the oldest geologic formations in the United States, some dating back to pre-Cambrian times (over 550 million years ago). The mysterious Pteridinium was a trilobite-like creature that probably lived at the bottom of shallow lagoons; paleontologists are unsure how this invertebrate moved, or even what it ate!
A close relative of Postosuchus, above, Zatomus was named in the mid-19th century by the famous paleontologist Edward Drinker Cope. Technically, Zatomus was a "rauisuchian" archosaur; however, the discovery of only a single fossil specimen in North Carolina means that it's probably a nomen dubium (that is, a specimen of an already existing archosaur genus).