I mean, again, the electric fence doesn't kill them, only hurts. You can set it to different voltages. It's a deterrent in the same way a skunk is - it just sucks to touch and there are easier things to get so they leave. It's going to have the same effect as thorns - they try to get through and OUCH so they leave. Anything that hits a coyote will hit a domestic dog, even the thorns. I know someone whose 10lb dog was chasing a rat and caught a small nail in the side and died from having pierced an organ. Nothing is 100% dog safe. (The african enclosures I refer to are called Bomas btw. And they can absolutely hurt a dog that goes running into them because they keep lions out.)
Honestly and frankly, I agree with the other posters - if you can't handle the thought of your dogs learning to mind the electric fence as countless dogs on farms have all across the world, and you can't shoot, and you can't trap.... Be prepared to lose birds.
But there's things you can try. Maybe not effective, but you can try.
There's also things like motion sensing lights for night time that mimic predator eyes.