Wikipedia says the earliest copyright for the song is a 1915 version by two African-American theater performers named Davis and Stafford [source: The Songs of Jimmie Rodgers: A Legacy in Country Music, by Jocelyn R. Neal, 2009 - page 124]

Anybody have any information on the Davis-Stafford version?

This (click) is apparently the 1943 copyright renewal. It attributes the song to Ed Stafford and Toots Davis, registered under the title, "He's in the Jailhouse Now." -Joe-