I'm kind of surprised to see so many guys opposed to handgun hunting. Granted, it seems we're talking pistols over revolvers, but we're also talking coyotes, not elk. Accuracy is the key, and accuracy IS attainable.
My wife took a nice meat doe this winter, calculated walking weight of 180-190lbs, at 43yrds with a 2.25" Ruger SP-101 and Hornady Leverevolution 140grn FTX, no exit, 50yrds and crumple. She hasn't gotten a shot on a coyote yet with it, but that's an active "work in progress".
I killed a couple doe about 15yrs ago on a bet about the effectiveness of 9mm on deer with a 9mm High point Carbine and a Kel-tec carbine. Frankly, I think a proper 9mm carbine would make a fantastic coyote rifle, and I'm hoping to see reasonable performance/reliability out of the new Taurus carbine (and a significant price drop), if so, I'll be hunting with one soon.
Back in college I killed over a dozen coyotes with a .22lr Ruger Mark II. Dogs were coming into our calf pens regularly (nightly) and were so comfortable, they'd drink out of the stock tank. I'd sit in the hayloft above the pens after I fed in the evenings and put rounds on them with my pistol. Most of these were under 30yrds, and many required follow up shots, but they dead was dead.
I'm not sure how many dogs he loses compared to recovers, but I've been getting pic messages from one of my cousins (college age) that has been calling coyotes using our grandpa's old H&R .22lr revolver this winter. Out of fear of overpressuring, he's not even using "mini mag" or super velocity ammo.
I'm prone to believe that most "standard" handgun cartridges will kill a coyote at any range you can really connect with it (call it 4" groups, just to put a number on it). 9mm, 40, 45, .357sig, 10mm, .357mag, 44mag, 45colt, etc. If you can get it there, there's a lot of bullet to do the job. Not looking at hydrostatic shock for DRT drops every time (except maybe shorter ranges with the badder cats on the block), but they'll do work. Naturally, the tiny tots like the .380acp, 22WMR, and .22lr, all have a bit stricter requirements, but they can work, assuming you can put it on target.