My dad sang a verse of a very similar song to me when I was small. It was:
Barney O'Flynn had no breeches to wear,
So they bought him a sheepskin to make him a pair.
With the woolly side in and the skinny side out,
It'll tickle my bottom, said Barney, no doubt.
The tune is:
DF# AA G E ED D D
DDD F# A D'D'D' C#' AAA
AA D'D'D' C#' A F# GABA
DEF# AAA G EE DDD
I think his mum sang it to him