Here's an English slow air:

Sweet Annie frae the Sea Beach Came

But Greene marketed it as a Scots song, and by the end of the century it effectively was, with the words forgotten and the tune only appearing in Scottish collections like Nathaniel Gow's "Vocal Melodies of Scotland". I included a version for the flute in my Scottish flute music CD-ROM.

I'd bet that if you played it on the flute in a typical session most people would think it was Irish.