Meade, Spottswood and Meade 'Country Music Sources' has an extensive listing of old-time artists recording this under a variety of titles:

Old Liza Jane - Uncle Am Stuart 1924
Liza Jane - Riley Puckett 1924
Liza Jane - Henry Whitter 1925
Goodbye Liza Jane - Fiddlin' John Carson 1926
Mountaineer's Love Song - The Hillbillies 1926
Miss Liza Poor Gal - Tenneva Ramblers 1928
Liza Jane - Carter Brothers and Son 1928
Old Eliza Jane - Doc Roberts and Asa Martin 1928
Liza Up the Simmon Tree - Bradley Kincaid 1928
Poor Mary Jane - Charlie Craver 1928
Liza Up the 'Simmon Tree - Bradley Kincaid 1929
Liza Jane - Kessinger Brothers 1931

--Stewie.