Not a parody, more of a quip, by Bob Newhart: “I don't like country music, but I don't mean to denigrate those who do. And for the people who like country music, denigrate means 'put down'.”
Actually I would choose the Stones "Dead Flowers", I love when they did that type of song with Jagger mangling the southern accents
"I'm Not in Here for Love (Just Yer Beer)" by Cledus T. Judd (Parody of "If You're Not Looking for Love [I'm Outta Here]" by Shania Twain)
Having produced at least 12 Country music parodies for various radio stations and morning shows myself, I heareby abstain.
I was at a show in Cincinnati where he did a slow ballad version of this song, with no Country touches in it whatsoever. Didn't even know the song was a Country parody, until it was released later.