Indeed songs weren't suppressed; they were the one thing that wasn't.

Here's a singing of Bunán Buidhe, though it's in English, in Thomas MacDonagh's translation - in the 18th century it would have been sung in Irish and unaccompanied, or perhaps accompanied with the small metal-stringed Irish knee harp. Oddly, I can't find a version in Irish online with the tune it's always sung to in Munster (that tune used in this English version), though there are Donegal versions to a different tune.

Or you might like The Night Before Larry was Stretched (sung here by Elvis Costell9) - a 1780s ballad in thieves' cant said to have been made in Dublin.