You can probably use any sort of old mountain bike or cruiser frame and just buy some big tires. If the roads are really bad, you probably don't really want a trackish frame anyway. The geometry is going to beat you up.

I've got a 1991 Specialized Rockhopper Comp that I converted to a single speed and put on Ritchey Moby Bite 2.1 tires and it's great for bad roads and a blast to ride. It's also pretty light.

If you get a wheel built with a White Industries Eno Eccentric hub you can basically use any frame you want. Just pick the tires and look for something with clearance.