The song is almost certainly from the time of the U.S. Civil War. The Mexican-American War was over almost before it started for one thing and the Civil War consumed vast quantities of human flesh so that bounties were paid to immigrants to enlist in the Civil War, for another.

25% of the combatants in the Civil War were born outside the U.S. and some 250,000 (the actual number will never be known) were Irish-born. One very readable book on the Irish in the Civil War is Paul Jones, The Irish Brigade (Wasington-New York: Robert B. Luce, 1969). There are others. I put 2 songs of the Irish in the U.S. Civil War and 1 song of the Irish in the Revolutionary War on the Folk-Legacy CD, "Irish in America: a Musical Record of the Irish People in the United States, 1780 - 1980." If the topic is of great interest to you, you might want to get a copy from Folk-Legacy. You can read more about the CD at... http://mywebpage.netscape.com/milnerconroy/irishinamerica.htm

All the best,
Dan Milner