Yeah you'll want a bigger caliber. 12 ga works good with #4 buckshot. any .223-.243 caliber are generally considered the best calibers for song dogs but if you don't care about pelts just use your deer rifle, whatever that is.
I'm serious, the best advice I can give you without writing a novel is to check out
http://www.predatormasters.com/forums and just read a lot of posts. Search for stuff like stand setup and call choice and what not. Most people ignore this tip I think, but it is the single most important thing I did to help point me in the right direction when it comes to calling coyotes.
My call recommendations:
Primos lil'dog (get the one with the Randy Anderson DVD)
Tony Tebbe's TT-Extreme (can be found on predatormaster.com or search Tony's website)
These two calls have produced more coyotes for me than any other (except one, it's custom)
Coyote/predator calling is not something you are good at immediately, it takes practice and more than likely you will be unsuccessful at first. Once you get it though, it is one of the more exciting things you can do. Good luck.
