Thoms, I'm new to this, as I've never shot a coyote yet. I hunt deer so take my post as that from a rookie. Responding as I just went through the same thing.
Tube size doesn't matter. Don't worry about it unless you already have quality rings you want to re-use. Biggest number to look at is the last one.. X50+ would be my recommendation for low light or night hunting.
As far as magnification. Personally I wouldn't go less than 3-9. I liked 4-16 and 5-20, but this would obviously be a personal preference. I hunt 3-9 on my rifled barrel shotgun for deer season.
My biggest recommendation would be to check the scopes out in person. I was fortunate enough to have good sales reps at Scheels and Cabelas that let me take the scopes to dark areas, or outside. The manufacture/ glass are incredibly different between manufactures. I'd say you really get what you pay for. I found it easiest to figure out my budget, and work backwards.
Good Luck!
