I know Pyramid State Park near Pinckneyville, IL allows upland game hunting, although I've never hunted for them there ... only waterfowl. Go to the IDNR web site for details. http://dnr.state.il.us/lands/landmgt/parks/r5/pyramid.htm#Hunting
. non-toxic shot is required.
I know that you have to have a free annual permit to hunt there, which you register for online. Details are on the web site too.
If you go, let me know how you do. - Bob