Some of my favourites, called to mind immediately -

There was a young man from Australia
Who painted his arse like a dahlia
Threepence a smell was all very well
But sixpence a lick was a fahlia.

There was a young lady from Crewe
Who said, as the Bishop withdrew
"I much prefer Vicar
He's quicker and slicker
And two inches longer than you"

There once was a man called McCool
Found a red ring round the end of his tool
He went to the clinic
His Doctor, a cynic
Said, "That's only lipstick you fool"

There was a young lady called Etta
Who fancied herself in a sweater
Three reasons she had,
To keep warm was not bad
But the other two reasons were better.

There was a young lady from Guam
Who observed, "The Pacific's so calm,
I'll swim out for a lark",
Then she met a large shark
Let us now sing the 23rd Psalm.

There was a young lady from Norway
Who hung by her feet from the doorway
She said to her young man
"Get off the divan
Cos I think that I've just found one more way".

...and there's more, later if required....