The National Seashore is open to hunting. In fact it's quite popular for deer. For coyote the only restriction they have is No Bait. Rifle is fine. The info along with where you can and can't hunt is on their website. The first time I went in there I went to the Visitor Center the day before to tell them I'd be in there seeing as it was mid winter, well outside traditional "hunting season", but coyote was still open.
After the expected mild anti- hunter sentiment at the front desk I was directed to the Enforcement Ranger, who told me they were quite the nuisance for him, where he thought the better spots were going to be, and his parting words were....kill them all.
I am glad I talked with him, I do try to keep it on the down low there, particularly spending the minimum time in the parking lot gearing up, however I did get busted by a jogger on the way out once who was more than a little startled coming across a couple camo guys toting rifles in the woods. She had to have gotten the guy I talked to when she called it in, as the next time I went there was a couple of big signs in the parking lot stating Yes hunting is allowed here, and Yes the season is open.
The population had been down around here, some disease went thru, but it appears to be up now. Good Luck, the Seashore is indeed a great place to hunt, the scenery alone is worth trip. In fact ya got me thinkin'......I just may give it a go later on this winter myself.