Here's a pre-Thorp reference, from the Buffalo [N.Y.] Evening News (Oct. 14, 1904), p. 12:

SONGS AND POEMS ASKED FOR.

Editor Evening News:

Please ask for the following songs: "Barney McCoy," "The Old Sod Shanty on the Plain," "Dying Darkey," "Ship's Carpenter," "The Dying Cowboy's Lament." The chorus to the last one runs something like this:

Once in my saddle I used to go happy,
Once in my saddle I used to go gay;
I first took to drinking and then to card playing,
And shot in the heart and dying I now lay.

                                                    Mrs. F. M.

Perry, Oct. 12, 1904.