Rory,
I hear what you are saying; however, please note that the Tyros 2 has a total of 23 country styles and I really don't know if among them there are some that would fit your bill.
Usually, when I play a style, I am able to guess the title of a song that would go well with that style; however, not being a country expert, I was unable to do this with these styles. I am afraid that I too have a stereotypical idea of country music (to me the quintessential country song is Tammy Wynette singing "Stand by your man"... ), but I guess that today there are artists like Shania Twain who would fall, more or less, into the definition of "country", and even Michael Buble's "Home" could be labeled as a country ballad.
So, the conclusion is that maybe you should try a Tyros 2 yourself and see what you think of it. By the way, I have tried to choose sounds that weren't too bad to my ears: the T2 has some really mean guitars (both acoustic and electric), and even the solo violin wasn't too shabby, was it?
Regards,
Andrea