Of course I'm talking more about mom and pop tourism like we have around here. Locally owned bed and breakfasts, small lodges, etc.
I'm not pushing it as "the solution"... but more as a general way to use the beauty of where they live to their advantage. Coal isn't coming back.
If they appeal to regional middle class tourism, however, it might pump some money into the economy.
Maybe rich hipsters on the coasts can be sold on paying thousands of dollars to spend a weekend living in a dilapidated mobile home alongside its native Eastern Kentuckian residents. Visitors will have an opportunity to sample local fare, including a lunch of cigarettes and a 64 ounce Coke from the nearest convenience store, and supper cooked by Maw-Maw, the family matriarch who will show you ways to fry things you never thought could be fried. You'll accompany natives in regional customs like serving as a middleman for black-market Oxycontin sales, mediating knife fights at the local watering hole, and serving as a character witness in your host family's pending child custody hearing.
Western North Carolina has similar issues with poverty- albeit without the coal problems- and has had some success catering to tourists from Atlanta and Florida. Perhaps Kentucky and WV could do the same for people from DC and Ohio.
An any case, the above post is rather horribly classist.