What about “Alligator Pie” …
Alligator Pie
Alligator Pie
If I don’t get some
I think I’m gonna die
Take away my (I can’t remember)
Take away my (rhymes with pie but I still can’t remember)
But don’t take away my Alligator Pie
Hee hee … that was my favourite book of rhymes when I was a kid …
Well, turns out the “woman of loose morals” interpretation is older than I’d thought, but I still think the KIDS would have been thinking of it as “slattern” while their parents thought “hooker.”
LAST MINUTE ADDITION: In 1664 Samuel Pepys used the word “slut” playfully, without implications of morality, to describe his daughter.
This lady walked into a bar, and she asked the bartender for a double entendre. So he gave her one! [rimshot]
I’ll bet she’d have loved this one then:
"Old Mother Hubbard
Went to the cupboard
To fetch her poor dog a bone.
But when she leaned over,
Old Rover, he drove her,
The dog had a bone of his own!
That would be Alligator Pie (1974), by Toronto native Dennis Lee:
The other two verses start with “Alligator stew” and “Alligator Soup” respectively, with rhymes to match. [It’s a copyrighted work, so I won’t post all of the lyrics. You can find them at the first link above.]
I first came across it in Toronto in the 1980’s when I visited the classroom of a friend who was teaching elementary school. We made a game out of it, encouraging her kids to extend the poem with new verses starting with things like “Alligator Cake” and “Alligator Bread”. We ended up with about ten verses.
Here is how I “solved” it:
I saw a peacock.
With a fiery tail I saw a comet.
Rain down hail I saw a cloud.
With ivy circled round I saw a mighty oak.
Creep upon the ground I saw a spider.
Swallowing a whale I saw the ocean.
Full of ale I saw a glass.
Sixteen feet deep I saw a well.
full of men’s tear that weep I saw their eyes.
All in flames of fire I saw a house.
As big as the moon and higher I saw the sun.
Even in the midst of I saw the man that saw this wonderous sight.
correct
Just got a book out of the library – Mother Goose’s Nursery Rhymes and Fairy Tales (Legacy Press, 1967). Get a load of this one:
Old Mother Goose, when
She wanted to wander
Would ride through the air
On a very fine gander
Mother Goose had a house
'T was built in a wood
Where an owl at the door
For sentinel stood
This is her son Jack,
A plain-looking lad,
He is not very good,
Nor yet very bad.
She sent him to market,
A live goose he bought,
“Here, mother,” says he,
“It will not go for nought.”
Jack’s goose and her gander
Grew very fond,
They’d both eat together,
Or swim in one pond.
Jack found him one morning
As I have been told,
His goose had laid him
An egg of pure gold.
Jack rode to his mother,
The news for to tell,
She called him a good boy
And said it was well.
Jack sold his gold egg
To a rogue of a Jew,
Who cheated him out of
The half of his due.
Then Jack went a-courting
A lady so gay,
As fair as the lily,
And sweet as the May.
The Jew and the Squire
Came behind his back,
And began to belabour
The sides of poor Jack.
And then the gold egg
Was thrown into the sea,
When Jack he jumped in
And got it back presently.
The Jew got the goose,
Which he vowed he would kill,
Resolving at once
His pockets to fill.
Jack’s mother came in,
And caught the goose soon,
And mounting its back,
Flew up to the moon.
I guess I know why they didn’t teach us that one at my nursery school!
Or:
Hickory dickory dock
Two mice ran up the clock.
The clock struck one –
The other one got away.
since “re-styled” nursery rhymes seem welcome in this thread, I’ll include my own (it’s from a book of children’s poems my two older daughters had when they were little):
There was an old woman who lived in a shoe
Which suited her fine when the winter winds blew
But when the hot summer sun
Got too much to handle
She packed up the kids
And moved to a sandal.
Well, if we’re going to be like that . . . 
"If seven whores without their drawers
"Were lying on the sand,
“Do you think,” the Walrus said,
“That we could raise a stand?”
“I doubt it,” said the Carpenter,
“But wouldn’t it be grand!”
And all the while the dirty sod
Was coming in his hand!
Little Miss Muffet
Sat on a tuffet
Eating her lox and bagels.
Along came a spider
And sat down beside her
And said, “What, no cream cheese?”
There was a girl
Who had a curl
Right in the middle of her forehead.
When she was good,
She was very, very good,
But when she was bad, she was great!
There was an old woman who lived in a shoe.
She had so many children, she didn’t know what to do.
Obviously.