You are right about the stockings I made a mistake... Me Dad has sung it for at least 60 years he is of Irish origin but I was born in England.
It goes like this
she had a pair of cotton stockins on her hair tied up with a ribbon on
I'm going to marry that little Irish girl

Thats the end of the song But he always finished with

Knees up Mary my fine daughter
Knees up Mary if you can
Knees up Mary my fine daughter and show your legs to an Irish man

I think it started something about courting and when he knocked on the door her Father wasn't in