In the early nineties I played in a group called The Piper's Hut. The group leader sang this song and his chorus went:

With me intwing of an ingthing of an iday
With me intwing of an ingthing iday
With me roo boo boo roo boo boo randy
And me lap stone keeps beating away

About five years ago I was in the band for a show called Fowke Tales about Canadian folksong collector Edith Fowke. This song was sung by one of the actors and his chorus went:

With me intwing of an ingthing of an iday
With me intwing of an ingthing of an iday
With me roo boo boo roo boo boo randy
And me lab stone keeps beating away

-making the second line a little bit irregular.
I like both versions, but find myself doing the first version.