You can always ask the local residents but there are private bird hunting preserves in the area..--->>>
https://stepoutside.org/plymouth-nc/hunting/Dare Game Land is large and a little more than 1 hour away, it's well known for bears, so there should also be small game there and adjacent land too:--->>>
http://www.carolinasportsman.com/details.php?id=4441Alligator River Game Land which is even closer could also be investigated.
Then there's the Alligator River National Wildlife Refuge that's open to hunting:--->>>
https://www.fws.gov/refuge/alligator_river/visit/visitor_activities/hunt.html"Game Animals
Only the following species may be hunted: ducks, geese, tundra swan, coot, quail, mourning dove, snipe, woodcock, rabbits, squirrel, opossum*, raccoon*, and white-tailed deer in accordance to Federal,
State, and local regulations. *Legal hunting hours for raccoons and opossums are from one-half hour before sunrise to one-half hour after sunset, unless authorized by Refuge Special Use Permit."
(May need non-toxic shot to hunt birds there)
See them on the map:--->>>
map