I suggest that "P for Patty" might actually be a variant of The False Young Man

AndyG

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THE FALSE YOUNG MAN

And `P' stands for Paddy I suppose
`J' is for my love John
And the `W' stands for sweet Willie-O
But Johnny is the fairest one

As I roved out on a May mornin'
A mornin' comin' clear
I leaned my head against the garden gate
To see two lovers dear

For to see two lovers meet my dear
And to hear what they might say
That I may know a little of their minds
Before I'd be on my way

It's sit you down on the grass he said
On the pleasant grass so green
It's been a long three-quarters of a year or maybe more
Since together we have been

Oh I'll not sit on the grass she said
Now or any other time
For I've heard that you're going with another pretty girl
And your hearts no longer mine

And `P' stands for Paddy I suppose
`J' is for my love John
And the `W' stands for sweet Willie-O
But Johnny is the fairest one

For when your heart was mine she said
And your head lay on my breast
You would make me believe with all of your deceit
That the sun rose in the west

So I'll not believe what an old man says
For his days'll not be long
And I'll not believe what a young man says
For he's promised to many-a-one

For he's promised to many-a-one she said
And many's the story he will tell
And when he's gained the pretty girl's heart
It's adieu pretty girl farewell

I'll climb a high, high tree he said
And I'll rob the wild birds nest
And I'll come down with wahtever I do get
To the arms that I love best

And `P' stands for Paddy I suppose
`J' is for my love John
And the `W' stands for sweet Willie-O
But Johnny is the fairest one

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Trad: Irish
The Watersons