The Howell First Reader, by Logan Douglass Howell, 1911, has:

Go tell Aunt Patsy;
Go tell Aunt Patsy;
Go tell Aunt Patsy
The old gray goose is dead.

The one she was saving;
The one she was saving;
The one she was saving
To make a feather bed.

Using Google Book Search, I found these variants:
"Go tell Aunt Rhoda" - 1891, 1909
"Go tell Aunt Nabby" - 1895, 1918
"Go tell Aunt Nancy" - 1897, 1909, 1913, 1916
"Go tell Aunt Abby" - 1906
"Go tell Aunt Rhody" - 1908, 1918
"Go tell Aunt Sally" - 1917
(Most of these are only references to the song, where only the title is given.)