"Garryowen" predates the ACW by quite a time, as does "Savourneen deelish" (sp?) and any Irishman who'd served in the British Army during or after the Crimea and before the ACW would have heard "Cheer Boys, Cheer" (although they would probably have changed the words slightly (I can't see Irish emigrants singing "Farewell England, much as we may love you").

I hope these fit your criteria.

Regards

Walrus