Not a parody, but somewhat about parodies. Nothing like all the regulars in a pub singing the "surprise" punch line along with you. No I can't remember the tune I used. (I only sang it once.)

Funny the First Time
(Me, circa 2006)

Sing, oh sing, that old song once more
Some people aren't sick of it yet
It's like hearing the same joke again and again
From some people I have met
I remember it as clearly as yesterday's lunch
But I'd like the chance to forget

It might have been funny the first time
Whether I laughed, I don't know
It might have been funny the first time
But I heard it so long ago

Poor Mary Ellen was sunk
Then she rose once again
And she's been dragged around, and up follows down
Like a glass of rot-gut gin
The first parody was amusing, perhaps
But it's been a long time since then

And there's holiday cheer, and poor Santa
They only come once a year
But how long can your grandma stay funny
Long after she's squashed by reindeer
The songs might have sleighed a decade ago,
But don't sing that one again here

There's dead dogs in cider, dead people in poop
Dead skunks in the road, and what's more
Can't swing a dead cat without a good song,
And we've got dead cat songs galore
One truth about people - the living - it seems
Is there's nothing as funny as gore.