Currently I am shooting a thompson center .204 and it has no trouble at all in leveling a coyote, and it is just a fantastic caliber to shoot. I have also used my .300 wm and shotguns, my dad uses his 22-250. But it doesn't matter what you use it only matters if you are enjoying it and killing some yotes.
I have a gp100 in .357 that i love to kill dogs with. I always carry it along with either my ar or my bolt gun. The choice of the second rifle depends on the area I am hunting. In easter WA. I usually bring the bolt gun in western WA. I stick to the ar, these choices are more baised on the rifles set up than personal preferance. The fn pbr is set up fro long range with a millet 4-16x55 optic. The ar however is set up with a decent eye relief for fast targeting. I built the ar from the floor up and set the optic plaform in a forward scout position. Seams to work well in the tight confines of western washington forests.
Howa 1500 in 22-250 is my go to gun on yodel dogs, with any reliable shotgun that will eat hevi shot dead coyote loads as a back up. Man I do love that stuff and they can be way out there for a scatter gun with it
Not so many predators over here but I run almost all bolt guns and shotguns even though I have permitted semi autos.
Foxes its a Mod 70 .222, Rem 700 .22-250 or T3 25-06 we dont keep skins .
For Wild dogs on the rare occasion I get to hunt them its the 25-06 or CMC .300win mag.
And Feral Pigs a major predator here its any thing from the 22-250 to the 450 rigby and the pump shotguns.
I also shoot a lot of feral cats but for those I prefer a .22 cal 40gn travelling at better than 4000fps like the 22-250 or a 220swift.
I guess I'm "Old School", so i only use bolt action rifles. I use a .243 with 87 vmaxes, a .223 AI with a 55 vmax and a 6AI with a 87 vmax. I got 2 .308's this year and am shooting a 110 vmax just for fun. They really blow up 2 liter plastic bottles at 200 yards!
If i want to save a pelt I like the .223 AI. If you dont hit bone, little bitty hole in, no hole out!
My best ever day on 'yotes was back in early 90's in NCentral SD while scouting for deer season. Saw 11 shot at 9 and killed 8. The back of my CJ-7 was a little ripe on that ride home. Remington 700 rechambered to 257 Wby