I searched for "Molly sweet Molly Malone" and found this. Not the song wanted, probably, but related?

From The pocket encyclopedia of Scottish, English, and Irish songs, 1816.
^^
MOLLY MALONE.

BY the big hill of Howth!
That's a bit of an oath,
That to swear by I'm loath,
  To the heart of a stone;
But be poison my drink,
If I sleep, snore, or wink,
Once forgetting to think,
  Of your lying alone.

CHORUS: Och! it's how I'm in love
Like a beautiful dove,
That sits cooing above,
  In the boughs of a tree;
For myself I'll soon smother
In something or other,
Unless I can bother
  Your heart to love me,
Sweet Molly, Sweet Molly Malone,
Sweet Molly, Sweet Molly Malone.

I can see if you smile,
Though I'm off half a mile,
For my eyes all the while,
  Keep along with my head:
And my head you must know,
When from Molly I go,
Takes its leave with a bow,
  And remains in my stead. CHORUS

Like a bird I could sing,
In the month of the spring,
But it's now no such thing,
  I'm quite bother'd and dead;
Och! I'll roar and I'll groan,
My sweet Molly Malone,
Till I'm bone of your bone,
  And asleep in your bed. CHORUS