The 2010-2011 IDNR hunting digest states that it is illegal "To hunt, shoot, pursue, lure, kill, destroy, capture, gig or spear, trap or ensnare, harass or to attempt to do so". Coyotes are protected as fur bearers in Illinois. I would contact your local district wildlife biologist for advice. You can find the DWB in your area at:
http://web.extension.illinois.edu/wildlife/professionals.cfm