Starting in about 1965, I have killed them with a 22lr, 3030, 12 guage, 22-250, 308, 3006, 243, 223, and a pickup. I have shot them beyond 500yds, and as close as 7 feet. Depended on how my calling and camo was working that day, and the individual coyote.
Which one is best? Well, they all killed coyotes, but my personal favorites and what I use today are the 223, and the 2506. The 223 is my favorite, as I like to try and get them into about 300 yds or closer, and it (the 223) is lighter and more portable, and being a semi, has a faster followup shot.
I can remember calling them up on the cellopane off a cigarette package, and when the Johnny Stewart record player (45rpm version) came out I thought I had died and gone to Heaven. Boy was that thing heavy. Then electronics and now BACK to mouth calls.
So! Calls, rifles, or calibers, it boils down to personal choice.