I fear you misunderstand. Silliness is no reason to reject a song from the canon of Great Fake Cowboy Songs, and "Ragtime Cowboy Joe" is a fine example. My mental ideal of a Fake Cowboy Song is one written in Brooklyn, which RCJ suits.

"Tumbling Tumbleweeds" is by Bob Nolan, the same guy who gave us "Cool Water." It's such a good cowboy song that I almost hate to acknowledge its fakeness-- but as Nolan was reportedly working as a caddy in Los Angeles when he wrote it, let's allow it!