I don't know when the tune "Molly St. George" was 1st called "The Coolin". BUCEM lists a song "Coolun with words" issued as a single sheet song with music by Anne Lee in Dublin, c 1780 (and later issues). The tune was usually found with the "Coolin/Coolun" title after that, and there are many copies. Bunting in his 3rd collection of ancient Irish music says that Lyons composed variations on the tune in 1702. The song commences "Oh the hours I have passed".