Not sure if this will help. Capitol State Forest is full of game of all sorts. Coyotes are suppose to be abundant in the southwest potion of the area which has a lot of clear cut land.
As far as camping goes, I believe the inside camp grounds are closed in the winter - however the rangers don't seem to mind much as long as you are being respectful to them and the land. Camp grounds on the edge of the forest are most likely to be accessible this time of year, but a little further from the safe hunting areas
There is the Evergreen Sportsmen Club at the entrance of Marksmen Dr, Little Rock/Bordeaux, that has camp sites. Call ahead to make sure. the club is on the edge of the C.S. Forest a few minutes from the clear cuts.
A good recon on Google-maps will be helpful, even better onX maps on a mobile device.
Hope this was helpful.