Thanks to a comment, I can update the Appalachian Writer’s Award. In existence since 1983, they had previously been missing on the internet, but now seem to have a spiffy new web-site.
Per its name, the award focuses on unpublished works focusing on Appalachia. They are sponsored by the Southern Appalachian Writer’s Assoc./ Culture Series. I didn’t find much info about specific criteria other than that, but there it is. If you’re looking for an previous winner to start with, I really liked Wilma Dykeman’s Tall Woman. Happy Reading!