Hadn't seen this one before but I saw this in a book:

There once was a man from Peru,
Whose limericks stopped at line two

and then later in the same book they had

There once was a man from Verdun

There once was a bard from Japan
Whose limericks never would scan
When told this was so
He replied, 'Yes, I know"
"But I always try and fit as many words into the last line as I possibly can."

there’s really no need to say more

The audience always wants more

There was a young man from south bend

Whose limericks all came to an end

Suddenly

Reminds me of an oldie:

“Roses are red, Violets are blue. Some poems rhyme, This one don’t.”

... he traded the fifth for a whore

... the four is an Int I adore

... three third bits is all I afford

Not a limerick but I want to share my favorite pun joke

I once submitted ten puns to a pun contest, hoping one would win, but
No pun intended

And this is the fifth line of four..

"...I can't think of a single word more."

whose limericks stopped at line four

Bad rhythm. Should be “whose limericks would stop at line four”

My bandwidth is crappy through Tor.

OR

Too much exposition's a bore.

OR

Though a quatrain's a ditty,

My pay's itty bitty.

If you cut prose apart, so as to make more,

Perhaps, one day, I'll afford my lost oar.

and then he said nothing more.

I find the fifth line a chore

You're both sadist and poetic boor.

And then he spoke not a word more.

There once was a mute man from spain
Who loved traveling on planes
When ask what he thought
Of the brand new concord
He said

And with that he walked out the door

*badum...* Y'know, no, this is so terrible, I will not finish the rimshot.

"Yer Mom was a ________"