Thanks for the help- yes the provos lullaby is the closest in words, but I take it that's a parody on the original given that my dad was born before 1920's and my grandmother before 1880's which is probably where he heard it or as a child at some family thing "over by".

So here it is with a teeny bit more pieced together

Go to sleep my little   (baby, laddie ......)
?While the time goes drifting by
Your Mother ..................
That's an Irish Lullaby

Any blanks or corrections gratefully received.