I think the new .17 WSM would be a great Predator/Coyote Caliber along with the .17 Hornet,.22 Hornet or the .204 Caliber!

Maybe You need to find an affordable Lease so You can Hunt Big Game/Deer and Coyotes in the Off Season?Here in Missouri we can go to several different Public Areas to hunt all types of Game.....it seems Illinios wants to get into the Hunters pockets for money before You can even begin to Hunt or learn the Sport of Hunting,they have so many Rules,Regulations,Tags Stamps and guide lines it's mind boggling!

How close are You to Missouri.....seems like You need to find a more Hunter Friendly State?

You may need to find someone that will take You Hunting or Mentor You into Predator Hunting.Most Farmers would love to have someone thin out the Coyotes...usually if You know someone for a while or earn their trust they will let You Hunt on their Property,others may require You to have some type of Insurance since they are in fear of getting sued!

Hang in there and keep at it....hopefully You'll get a straight answer about what Caliber is allowed and on which Public Land?