Actually, Makoshika State Park does allow camping. The sites with electricity generally require a reservation, but any site without electricity is fair game and first-come, first-served.
There's actually several other state parks in Eastern Montana, besides Makoshika (some that allow camping), and none of these are currently in any peril of going away.
Medicine Rocks State Park south of Ekalaka allows camping. However, this site has no improvements except a hand-pump for water and a few fire rings and picnic shelters.
(Sidenote - Pirogue Island State Park right here at MC used to allow camping but was changed to day-use only due to persistent vandalism.)
Way to the north, but still eastern Montana, Brush Lake State Park also allows camping and some sites have electricity.
Though you're getting a tad more central vs eastern Montana with this one, Tongue River Reservoir State Park also has copious amounts of camping - both with electrified and non-electrified sites. Not sure if it still is, but a few years back Tongue was the most heavily visited water-based park in the State Park system.
The only park in eastern Montana that's in any real danger of going away is Hell Creek.