There are several of these threads here on Mudcat, and there is at least one alternative chorus:

Ay, yi, yi, yi,
In Chili they do it for China;
Let's have another verse
That's worse than the other verse,
And waltz me around again, Dinah

And some of my favorite verses:

There was a young widow named Brice,
Who kept her dead husband on ice;
She said, "T'was hard when I lost him,
I'll never defrost him;
Cold comfort but cheap at the price."

There once was a pirate named Gates,
Who thought he'd do battle on skates,
But he fell on his cutlass
Which rendered him nutless,
And practically useless on dates.

There was a young lady from Bangor,
Who fell asleep while her ship lay at anchor;
She awoke with dismay,
When she heard the mate say,
"Boys, hoist up the top sheet and spanker."

There once was a poet named McNamiter,
Whose tool was of prodigious diameter;
But it wasn't the size,
Gave the gals the surprise,
T'was his rhythm – iambic pentameter.

There was a young maid from Madras,
Who had a most magnificant ass;
Not rounded and pink,
As you might think,
But t'was grey, had long ears, and ate grass.

There was a young man from Bombay
Who sailed to China one day,
Of the pox he did worry,
So he dabbed on some curry,
And for Ship Street his anchor did weigh!

There was a young man from the Bay
Who used to sing chanties all day,
He'd sing "Down Trinidad",
"Old Virginia" and "Sailor Lad,"
"Yankee John Stormalong" and "Ranzo Ray!

Cheerily,
Charley Noble