The guys from Troll Lord games are based in Little Rock, and I think they sponsor a convention (it was just held fairly recently, in fact).
Beyond that, I used to go to a convention in Fayetteville called Razorbattles, that was small, but friendly. And there is a convention in Joplin, MO. called Unicon that is probably in it's 5th or 6th year by now.
I know Tulsa has a regular convention, and I'm pretty sure Fort Smith has one as well, but I don't know their names.
I grew up in Russellville, btw.