First, It's pretty hard to trap a coyote. They mostly hunt alone but will at times hunt in small packs. About the only way to control them is to eliminate them or electric wires around the area where you keep your animals. I did eventually resort to electric wires around my coops and pens. My land is mostly open pasture but I did fence in an area and made pens. When your goats kid you can be sure the coyotes will be around. I have several game cameras on my property. Maybe this will help.The idea is a good one however I have more of a open pasture with a big run-in for my animals. So, it is harder for me personally.
http://www.plamondon.com/wp/faq-simple-electric-fences-chickens/ Good luck...
I think this mother is training her young not to mess with the electric wires.