First of all you
should call the Game Warden in your area and determine if it is actually a coyote kill. They get the blame but the reality is, neighborhood dogs kill far more livestock then coyotes do, especially this time of year. But so do bears, fox and Lynx, which is especially true of baby lambs and kids.
The second thing to realize that if it is coyotes, they are opportunist predators, they could care less about lambs or kids if there is a better meal that is easier to get like a fawn or bunny. With that in mind, no I have never had much luck with Electronet fencing; despite having a thousand feet of the crap given to me, I ended up giving it away to a person that was pretty desperate for sheep fencing. It is too short to stop anything from jumping over it, and most of the time, grass resting on it kept the stuff from giving a jolt to keep wooled sheep in or coyotes who were hungry out.
Keeping your livestock close to your house helps a lot as does penning them up at night. This is in part what I do and I have never lost a animal to predators, and Maine has the biggest coyotes in the world and a massive population of them here. We also have bear, fox an lynx and I don't have LGD's and run a commercial sheep farm.
My first defense is well constructed perimeter
fence. Page wire fence 4 feet high and always paying close attention to the bottom strand so it is tight and filling in holes where coyotes could possibly crawl underneath. While this is expensive, at $300 a lamb, so is losing lambs to coyotes!! t the same time, because this is considered a "coyote proof fence" if I ever do lose a sheep to a coyote, I will be compensated for the loss by the State.
Since I realize on rented land a high quality fence is not really possible, you may want to consider a LGD of another sort. I don't do it now, but I have run other livestock to combat coyotes. For instance I ran
beef cows with my sheep. coyotes will go after calf's but not cows because of their size. Add a few cows to your flock (or goat herd) and the coyotes may be intimidated. Keep in mind they are opportunists; make them think getting your animals will be harder then getting a bunny or fawn and your livestock will be more secure.
You should probably forget about taking a gun and shooting your way out of the problem, if again, it truly is coyotes causing the issue. They are strange in that the harder they are hunted, the harder they come back in breeding. And getting a killing shot off on a coyote on a dead run is almost impossible. Still hunting is one thing I employ here, but it is through good relations with my neighbors who are hunters. Not only do they have access to my farm, I have bulldozed roads through the woods so they can get from point to point easier and really encourage them to run their dogs and hunt coyotes that way. Its also what I don't allow to be hunted that helps. I don't allow hunting of Rabbit or
Deer here either because if coyotes are dining upon them, they are not dinning up my sheep.