I used to be play drums for 2 country bands in the 80's. The heads you use does not a country drummer make. I'd recommend single ply coated or clear if that's the info you're really after. But I'd like to share my thoughts on the subject as a whole.
There are a lot of threads asking which head for what style, and this always tickles me. From where I'm sitting, you can play ANY drumkit with ANY heads, in ANY style you want, authentically. If you gave me a massive Terry Bozzio drumset with 2 ply heads and all moongelled up, I could still play country songs and have it sound authentic. If you gave me a be bop kit w/ a 16" bass drum and high tuned toms, I could punch out a killer rock beat with it. If you gave me a 26" bass drum and massive power toms with metal type cymbals I could play a useable jazz feel. The kit doesn't matter. It's the players ideas that dictate the style. All this is my opinion only, but I'll bet there's many who will agree.
Country drumming isn't known for a lot of toms. (Generally speaking of course) Mainly, it just keeps the beat so the the singer telling the story can shine through. Country drumming is very supportive type playing and not showcased again, generally speaking. All you really need is a kick, snare, hi hat, ride and crash. Toms are not ultra necessary, but they're nice to have around for certain things. You can definitely get by without them, so the heads aren't that important, IMO.
Actually getting back to your question, I feel that for ANY style of music, single ply heads make the drums sound the best. Two ply heads, while they may sound good to the drummer, sound bad (unmiced) to my ear from an audience perspective. And don't get me started about muffling. I hate that sound with a passion. I'm sorry if I seem a bit flip, but in essense, this question makes about as much sense to me as "what is the best drumkit color for playing country?"