Also, i would be interested in hunting coyote with my contender, if there is anyone out there that knows where i could go in Illinois, i would greatly appreciate it!
It really helps to know someone although you are much more likely to get permission for Coyotes than for Deer or small game. I would suggest hunting the private ground when possible. You would have to target the smaller towns where friends or relatives live and get their imput on the local farmers or land owners that they know. In a lot of cases your friend or relative may pass as a (mutual friend) between yourself and the land owner which can make things much easier.
Once you do gain permission...don't be scared to help out a little around the place as you see the need. I have done everything from throwing a few bales of hay on the tractor skid for the feeders to helping round up and load hogs into a trailor for the market. The farmer really does appreciate your help and just might send you to his friends place a few miles down the road for more hunting.
If you can get your foot in the door of a community and the outcropping farms, pay particular attention that you keep gates closed and leave no trash. You must also never bring anyone with you unless it is approved by the land owner. Other particulars are that even though you have permission, You Do Not have a new private shooting range. Nothing will turn a land owner off quicker than the types that would (In Their Words)- (Would Shoot The Ground if it moved). A lot of these types just can't resist rattling off a few shots before they leave. They are often denied further permission because they are looked at as screwing around and being a liability.
If you are using calls (either mouth or elect) you have a big advantage. The tract of land that you are hunting might be marginal with the bordering tract where everyone is denied permission for everything being very good.
Some of these lands have been shut down for a very good reason such as equipment damage and theft. In other cases the owner may just state that No One Better Ever Hurt Any Of Their Animals. Make no mistake about this...No Land owner own's Any of the animals as they are State property.
While I greatly respect the no trespassing signs, there is No Law that say's the sound made from a predator call be required to do so!. The range of a mouth call is not real far but yet farther than you would think as I have had Coyotes come in at a dead run from over 200yds away even when using a short range call with it's tiny reed. The cold air really helps this and if you throw a Howler call into the mix, you may very well be talking to Coyotes from 1 to 2 miles out.
I hope that this helps out some and that you do gain permission. There is public lands avalible such as the Jim Edgar wildlife area NW of Springfield and more but most of these will restrict you to the shotguns with a .22 being ok.
In my opinion a .22 is not ok but think that the .17 hmr with the 20gr gamepoint or the .22 WMR would provide enough hydrostatic shock to recover Coyotes When Used Within 100yds.