Seems this one has some variation, I’d like to hear yours. I’ll go first:
Three Irishmen, three Irishmen, digging in a ditch
One called the other a dirty son of a
Peter Murphy had a dog, a brindle dog was he
along came another and bit him on the
cocktail, gingerale, 50 cents a glass
If you get hit with a bucket of shit be sure and close your eyes.
Just added the proper line to yours…
if you do not like it, you can kiss my
ask me a question, I’ll give you some advice
Three irishmen three irishmen digging in a ditch one called another one a dirty son of peter had a goat what a goat was he took him to the army to teach him company the goat got loose stole a goose sat on top of a rock along came a bumblebee stung him in the cocktail ginger ale 5 cents a glass if you don’t believe me kiss my dirty ass but no more questions I tell you no more lies if you ever get hit with a bucket of shit be sure to close your eyes. This is the one I learned
Three Irishmen (childhood rhyme - Best Version Ever!) circa 1974
Three Irishmen, Three Irishmen, digging in a ditch
One called the other, “You dirty son of a …
Peter Murphy had a dog, a fine dog was he!
He gave it to his girlfriend to keep her company.
She taught it, she taught it, she taught it how to jump!
It jumped up her petty coat and bit her on the
Country boy from Illinois, sitting on a rock;
Along came a turtle and bit him on the
Cocktail, ginger ale, five cents a glass!
If you don’t like it, shove it up your
Ask me no more questions, tell me no more lies,
A man got hit with a bucket of shhh it, right between
the eyes!
More Silly Rhyms - from those times!
The Hearse Rhyme (circa 1970)
<WARNING: MAY GROSS YOU OUT!>
If you see a hearse go by
You may be the next to die
They wrap you up in a bloody sheet
Then bury you down six feet deep
The worms 
crawl in
The worms 
crawl out
The bugs 
play pinochle in your snout
They eat your eyes, they eat your nose
And they eat the goodies between your toes
The pus comes out like whipping cream
And me without a spoon 
!