Here is a hog trap, you can get from Tractor Supply.
I gues you could build it yourself for a lot less.



The Voorhies Outdoor Products, LLC. Hog Trap is just the thing you need to help rid your land of any feral hog problems.

• High quality trap with 3 individual root type doors
• No trip wires to set, no springs or latches
• Hogs simply push through doors
• Easily fits into truck bed for transport
• 6 ga. wire mesh 4 in. x 4 in.
• 1.5 in. steel angle frame
• All welded construction

You could rig up a trigger, so when the coyotes get inside, the door closes.

Here is the link, so you can see if its worth it, or to build it.
---> http://www.tractorsupply.com/live-an...g-trap-5138476


Good Luck getting rid of the coyotes.