Country music is really forgiving ... the songs tend to be about the story-telling aspect rather than how well you deliver them, so that relieves at least some of the pressure.
It's also a very broad church. There's pretty much bound to be a number of singers whose voice you can emulate to one degree or another. There's a long list of country artists I can't get anywhere near, but I have no real trouble with Merle Haggard songs and I do OK with Hank Williams.
Singalongs where you just know the audience is going to sing the chorus for you are also helpful ... Take Me Home (Country Roads), The Gambler, Wild Side Of Life, you know the drill.