I'm sure they check for mice in between the bales of hay too... If there is an opening between the bales you could put a blind set there...Remember to place a stick or an object that will make them step where the trap is too... While your at it you could make this area an gang set...Just set quite a few traps there..You might get a double or a triple?

?Do a dirt hole, a blind set in between the bales.
You could go back with cable restraints if your qualified and saturate the area too...But you would have to place them away from the bales so the animals don't get hung up anyway....
Buckwheat is right you don't want a coyote hanging from the side.. Some small game hunter would just blast it and take it on you anyway then or if it's near roads the general public would freak out...