I recall reading in the glossary of a book of Folk Songs of the Miramachi, John Bonyan was quoted as saying that the reference to green in a song often refers to the woman being unfaithful. If that is true, Greensleeves referring to a prostitute or a coutesan wouldn't be far from the truth.

I like the idea of Greensleeves being a corruption of Irish, but I frankly don't see anything to back it up. The tune Cúnnla, otherwise known as The Frieze Britches is supposed to be sung to a varation of Greensleeves, though I don't see the resemblance. There do, however seem to be a number of tunes going by that name.

Sliabh an Ghrian would be Mountain of the Sun, but that would be the opposite of Greensleeves

Brían