Mentor
I would try rye. Rye, buckwheat, and hairy vetch are persistent and can be hard to get rid of once established. This can be a benefit in situations like this one. Good luck
Mentor
The grass is generally there if you take the dogs away and give it rest. But if you feel you want to plant something in the meantime, try to keep it very inexpensive on old prairie dog towns as they are usually on poor soils and struggle to get much established the first couple years. Cool seasons would probably do ok something like oats, triticale or rye, you could add some broad leaves, for diversity if it’s in your budget like flax and or clovers. I wouldn’t be afraid to plant these spring or fall just to get a living root and get the soil covered. If it’s in a pasture scenario, I would overlap the drill on the edges of the town and plant into the native grasses to promote the biology highway. Bale grazing this time of year on those sites would also be an option to provide some fertility and cover. Maybe find some baled up small grains to feed or native prairie hay from that area. Stay away from brome or crested hay.
SDSU Extension