Liland, I think your version came from a bad east Indian movie.

The earliest claim for authorship of "The Cowboy's Lament" is 1876, by Francis Henry Maynard. At that time he was working with "the Grimes outfit" wintering cattle on the Salt Fork of the Arkansas River On the Kansas-Indian Territory border. He said that he was inspired by "The Dying Girl's Lament," at the time sung by cowboys. He moved the scene from a hospital to Tom Sherman's barroom, a popular watering hole in Dodge City (The Whorehouse Bells are Ringing, Guy Logsden, 1989, p. 291, University of Illinois Press). The locale ws moved to Laredo later. Certainly the Bard of Armagh was known in the United States, and the tune came from this.
The traditional version was well-known by 1898 when Owen Wister included a verse in his great western novel, "Lin McLean." The many other lyrics, such as those mentioned by Bryant, are little known now and their occurrence or distribution in the United States is not well-documented.
In 1908, Sharlot Hall collected a version in Arizona:
"As I rode out to Latern in Barin
As I rode out so early one day,
'Twas there I espied a handsome young cowboy
All dressed in white linen and clothed for the grave."
The Irish origin is obvious here. The other verses were all similar to the Maynard-traditional verses (from the same source mentioned above).