Onnie,
Welcome to the Fire
With lots of books on the subject, there's a lot to learn, but here are just a few simple points....
I'd use the shotgun with goose loads over the 22. Dogs there can be larger from what I understand. Be aware of bobcats too.
For mouth calls, howlers, a rodent squeaker and rabbit calls are common. A rabbit call similar to the variety prevalent there is probably a good place to start....jackrabbit vs cottontails. Woodpecker or similar bird calls are also common, though I don't use those much.
Buy, beg or borrow some of Primos' DVD's on calling coyotes. Their calls are pretty good as well. Most of the bigger companies that sell predator calls have calls that will work.
Be stealthy when you are approach your stand so you don't get busted before you set up.
Setups are something that will take time to learn based on your terrain, but try to set up where you can see from higher ground, watch your flanks and be aware that the dogs will likely try to approach using cover, but will likely try to circle downwind to get a whiff.
In country with cover, it may result in close-quarters combat.
