"The Parting Glass" dates back to 1625 (for the tune) and a bit before 1800 (for the words), both in Scottish versions, but if you want to *call* it "The Parting Glass" you're using a title slapped on to it by an Irish singer in the last generation (who also changed a couple of words in the text).

Go back to older print sources and you can find something essentially indistinguishable but which you can know to be PD.