"Prairie Lullaby" was written by Billy Hill (1899-1940).

Written by "a young Billy Hill; (Jimmie Rodgers) "....had been doing fathers' lullaby songs... so the cowboy oriented turn in "Prairie Lullaby" (written by a young Billy Hill who would later compose pop hits "The Last Roundup"...)
From the book "Meeting Jimmie Rodgers:...", Barry Mazor( part on line).

In the welter of recordings, the composer became lost; the song appearing, among other places, in Hendron MS, no, 236, quoted in Fife and Fife, 1970, "Ballads of the Great West." Great West Pub.