The Online 78-rpm Discography Project lists the following recordings:

[I'm not sure these are all the same song, or that they're even related; I selected them only for the similarity of their titles.]

Haydn Quartet, ONLY A MESSAGE FROM HOME SWEET HOME, Victor 4561, 1905.
Haydn Quartet, ONLY A MESSAGE FROM HOME SWEET HOME, Victor 16801, 1910.
Charles Nabell, THE LETTER FROM HOME SWEET HOME, Okeh 40252, 1924.
Ted Chestnut (a.k.a. Cal Turner), LETTER FROM HOME, Gennet 6480, 1928.
Alex Gordon, A MESSAGE FROM HOME SWEET HOME, Conqueror 7269, 1929.
Billy Vest, A MESSAGE FROM HOME, Columbia 15602D, 1930.
Asa Martin & James Roberts, A LETTER FROM HOME SWEET HOME, Banner 32703, 1933.
Christine Rangers, A MESSAGE FROM HOME, Decca 5935, 1941.
Connie Boswell, JUST A LETTER FROM HOME, Decca 18483B, 1942.
Hank Penny, A LETTER FROM HOME, Decca 29597, 1955.