Here's a YouTube video of Tony Cuffe singing this:

https://www.youtube.com/watch?v=acCBvF-VYdE

I've typed out the notes in Noteworthy Composer. This is in the key of G.

G Oh the springtime re-
D* turns to the
Em lagan a
D* -gain And the
G lark sweetly
D sings o'er the
G green fertile
D plain and I'll
G tak' the
D* road that is
G dearest to
D me The
G road to
D Drum-
G leman that
G winds tae the sea.

The intro has dissonances and complex chords, but when he sings, the harmony is simpler, as above. There are three places (*) where the notes of the melody are C-B-A. Well, no chord goes with that. I simply tried a D chord, letting the C note make it a D7 and stepping carefully during the B. You might try a D7.

Some commenter on a YouTube said that name of town isn't Drumleman, it's Drumleghbhmvan (or similar.) However, any streetwise folkie knows that 'leman' is middle English for sweetheart, and that Drumleman is the stuff of fantasy.

Although it's been a while, thanks all for the pretty tune.