“What’s the best gun/ammo for coyotes?”
How dead do you want them?
How close do you want to get before pulling the trigger?
A Ruger 10/22 with Winchester Expediter screaming out of it at 1640 fps works.
If you can find an older Ruger 10/22 in .22 Magnum, that will work too.
But a good varmint gun using .223, .270 or so will also work, but you have to watch for over penetration punch through.
But I’m the guy who’d use a .308 or a .338 Lapua on a woodchuck, so don’t mind me.
I used a 12 G slug shot on a bowling ball once
Long ago when I was kid, my great uncle (long since deceased) was using 30-06 on groundhogs that were eating his garden. I thought it was a good idea. You didn’t have wounded ones running back into their holes like if you shot them with a .22. He sold produce, so the were eating his profits.
If it takes a second shot, I can deal with that.
How close do you want to get before pulling the trigger?
Pretty close (see post 7). If I'm not sure the round won't carry to my neighbor's property, I'm not squeezing the trigger.