I found descriptions of a couple more (but I don't have a recording, or sheet music, or lyrics):

GET OUT AND DIG, DIG, DIG
"A Feature of the Blue Network's National Farm and Home Hour."
Words and music by Hunter Reynolds.
Chicago : Skokie Music Co., ©1943.

First line of text: Get out and dig dig dig in the sunshine.

Copies of the sheet music are held by University of Missouri-Kansas City; Bowling Green State University, and Brown University.

- - -

DIG-DIG-DIG : (DIG A LITTLE GARDEN FOR VICTORY)
Words and music by Milton Leeds and Billy Hayes.
New York : Bob Miller, Inc., ©1943.

[First line of verse:] Farmer's in the dell, working night and day.
[First line of chorus:] Dig, dig, dig a little garden, in your own vicinity.

A copy of the sheet music is held by Bowling Green State University.