Greg:

The version I first learned had the chorus beginning:

"Aieeee, aieeooo, me laddie, lie easy
Sure my misfortune is none of your own.
And it's weary I am with weepin' an' mournin'
And rocking the cradle of a child not my own."

THese are phrases that are typical not of English, IMHO, but of the anglicized Irish. I can't imagine an Englishman writing "Aieee, aieeyo" unless he was trying to imitate Irish -- as in my "Tin Pan Alley" hypothesis above. Nor start a sentence with "Sure".

But as I said earlier I am not expert in these matters, just a happy amateur! :>)

A