We have two definite tunes for texts posted so far; as ever, midis will be available via the  South Riding Folk Network  site until they appear at the  Mudcat Midi Pages:

The Holly and Ivy Girl (Carolan's Lament)
Monks of the Screw

The first is made from notation for John Keegan's song in The Irish Song Book (A.P. Graves; second, revised edition, 1895), and the second from the tune provided by William H. Curran, and printed as #490 in Stanford-Petrie, The Complete Collection of Irish Music 1903.  A few notes in the first two bars have been split into two in order to accommodate the lyric given.