I have always understood that Maggie Cockabendie was a Dumbarton song. Certainly I heard it sung in the 1950s by some Dumbarton people and the places mentioned in verse 3 are the names of places in Dumbarton (e.g. the Vennel was an old street in the town--I don't know if it still exists--and the Quay was, well, the quay).

These are the words I know:

O Maggie Cockabendie
she's a lass that I admire,
curly hair, I'm awfu shair
She sets my hert on fire.
Now Maggie tak's the biscuit
And oor Maggie tak's the bun
When Ah gi'e her a wee bit beardie
on the stairhead jist for fun.
    She's ma peerie weerie weerie weerie winkle,
    Ma jeely and ma jam,
    Ma fairy, ma canary,
    Ma bonnie wee bit lamb.
    She's ma bunch o' sourocks
    And ma laughin' cockatoo,
    An' I'll be Maggie's cockabendie
    cockaleekie loo.
They say that Maggie's got me
Oan the end o' a wee bit twine.
They say when get merrit
She'll mak' me toe the line.
Now Maggie's no' a lass like that,
She's modest and she's braw.
And I'll be Maggie's cockabendie,
cockaleekie law.
    (repeat refrain)
They see when we get merrit
In a year or two or three
We'll settle in the Vennel
Or maybe doon the Quay,
And there we'll sit and whistle
Till the ebbin' tide is law
And play a bee-baw-babbity
Tae pass the time awa'.
    (repeat refrain)