The Petit Jean in the Ouachita Mountains...
Your not going to find any CW sites that are well marked or even known. There was a ton of CW activity, but no one cares since it ain't Prairie Grove or Pea Ridge. Cause let's be honest, those battles and Jenkins Ferry are the only ones in Arkansas anyone ever heard of or thinks happened in the grander scheme of things. Which I find annoyingly ignorant of a very rich history. (No offense people, it can't be denied that folks completely ignore it.)
There was a lot of skirmishing in the area, and a lot of bushwhacking. Waldron was even burnt by Federal troops, and I think there's a small private CW museum/gun shop there. Or at least I've heard there is. South of the Fort Smith area there's also the Devil's Backbone battlefield.
Somewhere on the site is a thread I did on thenwar in the region, and I know JamesN had a thread. Both could be helpful, there's also a couple blogs and websites by the guy who wrote the book on Massard's Prairie detailing the war there, even the Petit Jean area, a Google search ought to bring it up.