I wouldn't use anything smaller than a .22 mag for a rimfire gun, I would be worried about bullet "splash" the 17 mach and hmr but I'm not sure what is available as far as suitable coyote ammo. I could be wrongas I don't have one and don't stay up with availabe rounds.Centerfire you could use anything from the .17's on up. It is all about bullet selection and what you want to do with the hides I suppose.I use an AR15 in .223 made by Dtech if you are looking for a AR I highly recommend him he makes very nice guns and he is on predatormasters just do a search on dtech. I also use asavage model 12 bvssthey areawsome guns for the money. I sold my abolt and do not miss it at all.I use a 12 gauge shotgun also. Warning AR's are very addictive the only reason I still use a bolt gun is because AR's are illegal in my county. Have fun.