I found this parody that Adam Sandler sang, accompanied by Paul Shaffer on piano (who also "echoed" a few words on some choruses) at Madison Square Garden in New York City as part of "12-12-12: The Concert for Sandy Relief," on December 12, 2012. This article in Rolling Stone implies it was the first ever parody of "Hallelujah."

My transcription from YouTube:


SANDY SCREW YA
Words by Adam Sandler, music by Leonard Cohen, "Hallelujah"

The terror of the hurricane,
The unforgiving wind and rain—
New York, the world held its breath as the storm took it to ya,
But you've been knocked down in the past,
Taking shots they thought would last,
But you always get right up shouting "Hallelujah!"

Hallelujah!
Sandy, screw ya.
We'll get through ya,
'Cause we're New Yorkers.

Yeah, New York, you've dealt with crap before,
Like squeegee men and tunnel whores,
And restaurant delivery bikin' right through ya.
They'll puke on your stoops ev'ry Sunday morn,
Times Square losin' all its porn,
Original Ray's Pizza closin' too, ya.

But hallelujah! (Hallelujah!)
Sandy, screw ya! (Screw ya!)
We'll get through ya (We'll get through ya)
'Cause we're New Yorkers.

'Cause we believe this too shall pass,
Like when Sanchez fumbled into an ass,
And during the playoffs, A-Rod telling girls in the crowd, "I wanna do ya."
The Mets have sucked since eighty-six.
Isaiah tried to ruin the Knicks.
But now Jason Kidd and the boys can freakin' school ya.

Hallelujah!
Sandy, screw ya!
We'll get through ya,
'Cause we're New Yorkers.

The bedbug scare of two-thousand-ten,
The Lohans getting busted again and again,
The lady who said she was a man right after she blew ya (sorry, that was just me!),
Trump's comb-over always makin' us sick,
The congressman who tweeted his dick,
The mayor's ban of thirty-two-ounce Mountain Dew-ya.

Hallelujah! (Hallelujah!)
Sandy, screw ya! (Screw ya!)
We'll freakin' kung-fu ya (kung-fu ya),
'Cause we're New Yorkers.

And Jersey, you've taken your share of hits:
The situation only showin' his tits,
The Turnpike Exit Thirteen stinkin' like poo-ya.
You lost the Nets and now they're good,
But we're still the Hudson brotherhood.
Together we'll give Sandy a big fugooya.*

Hallelujah! (Hallelujah!)
Connecticut too, ya (too, ya).
We'll get through ya (we'll get through ya),
'Cause we're New Yorkers.


* Fugooya = my phonetic spelling. I'm sure he meant "fuck-you, ya" but he seemed to deliberately slur it.