I second Will's suggestion of the "Star of the County Down" family.

Many, many variations.

The one popular today is essentially that of an American minstrel song of the 1850s, "The Boy with the Auburn Hair" - but that had totally ridiculous lyrics.

Not to say the tune started there(it seems utterly out of place), only that it's very close to the one internationally recognized as carrying a very different song.

A Confederate officer named C. W. Alexander wrote "The Southern Soldier Boy" to the "Auburn Hair" tune in 1863. It's become a standard among Civil War aficionados.