Here's one I heard recently related to COVID, among other things. It's more of a current events song but it definitely mentions Covid a few times. I really liked the wordplay in the song--it's a lot 'smarter' than many of these parody songs tend to be.

JP Harris - Take Off Your Tinfoil Hat (listen)

Well, I read on Reddit that the Reds are commin'
And by Reds I mean Blues that are secretly Commies
That were posthumously hired by Hugo Chavez to alter ballots
And the theory holds water if you don't overthink it
The water is a Kool-Aid, so don't ever drink it
And I only trust news that is tailored to my discerning palate

Did you know Q is the 45th letter in the alphabet
And that's how I know the 45th president
Sends secret codes in 45-character tweets
Oh, and D-Day's comin' and I'm armed to the teeth
Against tyrannical government except when I think
They need my unsolicited help quelling people's freedom of speech

CHORUS

So take off your tin foil hat
Don't you know that it's out of fashion
Don't you know that Jesus has found
All the ammo that you've been stashin'
You believe that 5G's
Comin' in the night to take your babies
Away for the Satanist hordes--good Lord!
Y'all must be bored, you need to get off the internet

Oh, the virus is fake, so I'm goin' to the beach
And a mask makes you wanna have sex with sheep
And I'll shoot you if you stop me from gettin' drunk over at Chili's
Oh, I've read between the lines, or at least every 20
I skimmed the report, somethin' seems funny
And the proof is all there, I just don't have the details, really

Well, global warming's a hoax from a super-computer
To take all our trucks and make us drive scooters
And micro-chip the masses, I just know it to be so
I want the freedom to die in a senseless mass shooting
I heard Obama was payin' the protests and looting
And the proof is in the basement of the Alamo

CHORUS

Oh, I said Lord--Good Lord!--you need to get off
Stay off
Get gone
From the internet