Not sure about coons and yotes, but they are great for rabbits. A single or even a pack of beagles would be in a tough situation against a coon or coyote. The most difficult thing to accomplish would be to train the dog to run all three animals when you want it too.
As for rabbits try and find an older rabbit dog to let your pups run with. Also dragging a fresh dead rabbit and doing the same evasion tactics rabbits use to get away from dogs and let the dogs find the rabbit and then treat them.
I used to have a pack of beagle about 9. i ran rabbits with them. they are very good dogs to have and grate around the family. i still have two but the dont hunt any more. they were very easy to train.
I love working with Beagles. The few I have trained have all been fairly easy, its just a matter of spending some time out in the field. Started her as a pup by locating a rabbit(in the summer they practically invade my neighbors yard) and trying to get close enough for her to see it. If that doesn't work I'll put her nose where the rabbit was sitting. Just alittle at a time. Its alot of fun to watch her put everything together and run a rabbit in the circle.
I must admit that I have missed a big game animal with a rifle. And not only was it a bull elk, it was the largest bull that I have had in my sights with a tag in my hand. But, as with most "missed shot" stories, I have an excuse. Moisture doesn't really ever bode well for hunting equipment. When moisture (either rain or snow) gets into a firearms barrel, nothing good takes place. A couple rain drops down there can change the point of impact drastically and a barrel jammed with snow after a...