There are a whole bunch of Blackbird tunes, but so far I can't find The Blackbird and His Mate; couldn't be the same as The Blackbird and the Hen, by any chance?

I forgot to mention that there's a Gaelic set of An Draighnean Donn, spelt with an a this time, in Peter Kennedy's Folksongs of Britain and Ireland; it was recorded by Noel Hamilton from James Meenan of Baile Thiar, Tory Island, Donegal, in 1967.