I have this as

A maid went to DUBLIN her markets to learn
To sell for her mammy three hanks of fine yarn
She met a young man on the king's own highway
Which caused this fair damsel to dally and stray

Come sit down beside me, I mean you no harm
Come sit down beside me, this new tune to learn
Here are three guineas your mammy to pay
So leave off your learnin' till the next market day [I hear "yearnin" but learning makes more sense]

She sat down beside him, the grass was so green
The day was the fairest that ever was seen
"The look in your eye beats a morning in May
I could side by your side till the next market day."

But as she went homeward the words he had said
And the tune he had sung her still rung in her head
"I'll search for that lad, be it night or by day
Till he learns me the tune of the next market day."

Can't recall whose record it was on, maybe Offbeat Folk Songs? Maybe Shep Ginandes? Male, American, at any rate.