Think this is the one you're looking for, as sung by the late Michael 'Straighty' Flanagan from Inagh, Co. Clare (recorded in 1975)
Jim Carroll

SPRIGHTLY YOUNG DAMSEL.
Michael Flanagan, Inagh.

I'll sing of a sprightly young damsel who lived in the county Kildare.
She was pretty, quite charming and handsome; her features were blooming and fair.
Her parents had great store of riches, she was sprightly and funny with all.
But at night she was quite discontented with her face turned up to the wall.

She got up very early one morning, complained of a pain in her head.
She dressed herself cosy and warm and called her mamma out of bed.
She says, "my dear mother I wonder why my tears do abundantly fall;
Every night I do lie cold and shiver with my face turned up to the wall".

She says, "my dear daughter be easy, I guess what's the cause of your woe.
Won't you marry Sean Moore the fat miller who lives in the valley below?
For he has both money, land, riches, a well furnished kitchen and hall.
And with him you never need grumble with your face turned up to the wall".

"Don't you know my own darling Willie, who lives down at the lake?
His heart is both mild soft and tender, he used me both early and late.
I'd rather my own darling Willie without e'er a penny at all,
Than thousands with that dusty old miller who'll leave me lying cold to the wall".

"Don't speak any more about Willie", her mother this instant replied.
"For 'tis neither my will or intention that you should be ever his bride.
For he has neither money nor riches nor bacon in kitchen or hall.
Nor is he the man I intended to keep you at night from the wall".

"Ah", she says, "my dear mother I wonder why you should such nonsense uphold.
I find a great change in your temper, and crazy as you're getting old;
For when you were youthful and merry, you'd give money, land, riches and all
In to some sprightly young fellow who'll keep you at night from the wall".

At this the poor mother relented and seeing her dear daughter in grief,
And soon she quickly consented to give her mind ease and relief.
And then she prepared a grand wedding, rice puddings, punch, whiskey and all
And married she was to her Willie, who rolled her far down from the wall.

"I think it far better in winter when Willie goes off to the plough;
Go and get up his pail and his *piggin, and go milk his one horned cow.
Than thousands of money, land, riches, and bacon in kitchen and hall,
Than to lie with that dusty old miller who'll leave me lying cold to the wall"

*Piggin:- A small wooden bucket with one stave projecting above the rim for use as a handle; (also called "pipkin").

We have been unable to trace any other version of this, either in print or sound.