Here's the Texas Parks & Wildlife site for public hunting. They offer all sorts of hunting opportunities from draw hunts to walk-in hunts.
http://tpwd.texas.gov/huntwild/hunt/public/Another option is to advertise in some of the area feed stores just to the north and or to the west of CC looking for any leases that have slots to fill. Expect to pay a pretty penny to hunt on a lease though.
