RE: Coyote gun... (help)
Any of those guns could work. If you can hit them they will kill them. #6 shot shot I personally wouldn't use. If you can get them in close enough buckshot will definielty put them down.
I use a 22 mag to shoot coyotes with and I only shoot Winchester Supreme jacketed hollow points through it.
Sounds like you have a lot of options.
Happy hunting.