The Union Base Ball Club March, dedicated "To the Members of the Union Base Ball Club - Champions of Missouri," was composed by T.M. Brown and published by Richard Compton in 1867. Brown is listed on the cover of the sheet music as an honorary member of the Union Club and Nineteenth Century Baseball Photographs On The World Wide Web mentions that he was "captain of the Third Nine."
According to the Robert Edwards Auction website, the cover for the sheet music "features nine beautifully engraved portrait images of the Union team members on the front. This is one of the earliest of all baseball sheet musics, and is also one of the first to picture actual likenesses of prominent ballplayers. The engraver's name (F. Welcker) appears in the lower left." A matted and framed copy of the sheet music in excellent condition sold for $1,276 in 2006.
While information on the composer of the music is scarce, there was a prominent Missouri financier named T.M. Brown who was a partner in the Brownlow & Brown banking firm in the 1880's. While more research is needed, it's possible that the two men where one and the same.
The sheet music for the Union Base Ball Club March is posted below for anyone with a musical inclination. I would certainly love to here what this music sounds like.