If you want em dead and pelts are not a concern I recommend a 223. Mine is a Ruger M77 MKII stainless varmint. The load I shoot is Viht N120 24gr, Rem 7 1/2, and a 40gr V Max(depending on the gun I've had velocities of 3900-4200fps). If you want to save pelts the 204 Ruger may be a little better. My load for that is 28.8gr of Viht N540, Rem 7 1/2, and a 32gr V Max. Better BCs with the 204 but much cheaper reloading or buying the 223 ammo.
For my calling gun I built a Rem 600 Pac-Nor #1 ss in 6x45mm. Synthetic stock a Leupold 1x4 VX-II. Very accurate 55NBT H-335. It is a little messy on fringe hits but they don't run.
My vote goes to my favorite rifle period....16" AR-15 The best part is you're covered for 2-legged AND 4-legged varmints...
Biden's most truthful quote ever came during his first press conference, 03/25/21. Drum roll please...... "I don't know, to be clear." and THAT is one promise he's kept!!!
Get the one you can hit the things with. I'm thinking that that new Les Baur 6.5 Grendall AR 15 would be nice to try.....and it would give me an excuse to buy one!
Really though, I have an AR 15 in 223 that works pretty good for them (and lets face it, it's fun to shoot them with). I bought a CZ bolt action in 17 HMR with a 6 to 12 x scope just for coyotes, and it works pretty good too, especially if they are inside 200 yards. I bought a Remington 700 in 25-06 a few years ago for longer range varmits. It does it (well) though it is a little loud.
For the targets of opportunity you just can't beat my 444s. While it is loud and kicks a mite (why have a 444 that doesn't?), the coyotes under 150 yards just fall over dead when they see it. Just the sight of it in the field scares them to death.
I use my PD rifle for driving around coyoting . Rem 722 in 22 250 AI with Pac nor 22 inch and FX 12 Loopie .50 gr Bitzkings .
For open country calling , a 700 SA BDL with Shilen in 6 MM AI . 4.5 X 14 Loopie . 70 gr NBT at around 3800 .
Nightime and brush calling I use my A Bolt Hornet as it came from the factory except for trigger work . 3X9 Vari X 2 . It likes Speer 40 gr. .223 and Lilgun .
I don't save coyote hides. Mine is a custom- Rem 700 stainless action, that is trued. 26" Lilja stailless barrel, number 4 contour McMillan Rem hunter stock chambered in 240 weatherby scoped with a Leupold 4-12X