Hello, Joe. I haven't found the sheet music, but I did find this info, which might prove helpful. This is what ragtime pianist Perfessor Bill Edwards has to say about 'Ragtime Cowboy Joe.'

"Lewis F. Muir, Maurice Abrahms (M) and Grant Clarke (L) - 1912: I actually grew up thinking that this was an original song by David Seville and the Chipmunks, and the older I got the less likely I thought that it was actually a ragtime era piece. Then I got a request from a fan to post it here. My first thought was that the request that fell outside the parameters of what I generally do. Ooops. Not only is it an authentic ragtime tune, it was penned by no less than three of the better songwriters from the era. Notably, Muir would write the tune for Robert E. Lee that same year. Actually, with the original verses intact, it's a cute and clever novelty piece."

I downloaded Bill Edwards' MIDI of the song, but it is unusable for me - a welter of notes and rests of bizarre lengths.