A list of tunes played in Indiana in 1895 includes "Rockback [sic] Davy." "Rock Back Davy" is mentioned in Kentucky in 1883.

Other examples:

The Detroit Free Press in 1884: "Rock back Davy, Daddy shot a bar, Shot him in the eye-ball, Never touch a har."

New York Saturday Journal (July 1, 1871):

"Rock back Davy cuttin' up a shine,
Gal with the red ha'r kicikin' up ahind!"

The latest mentions of the tune I've seen are from Texas in 1907 ("the familiar tune 'Rock Back Davy'") and from California in 1934, where it's paired with the long-familiar "Money Musk."