For many copies of its tune see "My lodging is on the cold ground" in the Irish tunes index on my website. The tune is B316 there. The original "My lodging is on the cold ground" song and tune (B315) were of the 17th century, but in 'Vocal Music or the Songster Companion', 1775, the new tune appeared (repeated with the song in Corri's 'Select Collection', c 1779, and in 'The Vocal Enchantress', 1783). The tune appears as that of "I loe no a ladie but ain" in 'The Scots Musical Museum', #267 (1790). Moore's song was of 1807 or 1808, there's some question about the exact date. The copy of the tune in Aird's 'Airs', I, c 1778, can be found via the web-wide ABC index.