Well I found it. It's called Green Mossy Banks of the Lea. There is a similar song in the DT from the MacKenzie book
GREEN MOSSY BANKS OF THE LEA
#77 Songs and Ballads From Nova Scotia - Helen Creighton
Dover Publications - 0-486-21703-5
Library of Congress Catalogue Card # 66-26823When first to this country a stranger
Curiosity caused me to roam,
Over Europe an exile I wandered,
Far away from my 'Merican home.
Till at length I arrived in sweet Erin,
The land which I long wished to see,
And my footsteps seemed guided by fairies
On the green mossy banks of the lea
One morning of late as I rambled
Where the sweet winds from heaven did blow
'Twas down by a clear crystal river
Where the sweet running waters did flow,
It was there I espied a fair damsel,
Most modest appearing to me,
As she rose from her seat near the water
On the green mossy banks of the lea
I stepped up to bid her good morning,
Her fair cheeks they blushed like the rose,
I said then, "Those meadows are charming,
Your escort I'll be if you chose."
She said, "Sir, I never need any escort,
Kind sir, you're a stranger to me,
But yonder my father is coming
On the green mossy banks of the lea."
I waited till up came her father,
I picked up my courage once more,
I said the, "If this be your daughter
She is truly the girl I adore,
Ten thousand a year is my fortune,
A lady your daughter shall be,
She shall ride in a coach of six horses
On the green mossy banks of the lea."
They welcomed me down to their cottage,
Soon after in wedlock were joined,
'Twas there that I rented the cottage
In splendour and grandeur divine
So now the American stranger
Right pleasure and pastime to see,
With his adorable, gentle Matilda
On the green mossy banks of the lea
Come, all pretty maidens, take warning
No matter how poor you may be,
There's many a poor girl that's handsome
As those that has large property.
By flattery let no man deceive you
No matter how poor you may be
Be like adorable, gentle Matilda
On the green mossy banks of the lea
See MacKenziie, No. 47; Journal, 11, 150, and compare Pretty Girl Milking Her Cow. Cf. also Hannaghan, The Book of Irish Gaels, The Old Bridge at Toor.