"You're Only Second Rate", the Villain Song from The Return of Jafar is a swingy Broadway-style song that contains some elements of this.
We are talking about the perversion of a home created by two Monster Clowns after all.
Batman Beyond: Return of the Joker uses an offscreen music box to similar effect.
Bonus points for occurring in an actual circus of sorts.
Coraline has an excellently creepy scene with the Other Kangaroo Rats.
This is quite fitting for a Monster Clown singing about insanity to a man being forced through a carnival dark ride.
Batman: The Killing Joke: " I Go Looney ," the Joker's written Villain Song from the original graphic novel about succumbing to madness in times of stress, is imagined here as a deranged carnival-ish tune, with a bit of a vaudeville showtune aesthetic as well.
Pinocchio and the Emperor of the Night: The infamous Nightmare Fuel scene in which Puppetino transforms Pinocchio back into a wooden marionette by playing a sinister, chaotic carnival music with a cursed organ grinder.
This turns out to be fitting, because the circus is a trap to kill Ken.
Chargeman Ken!: "Waves of the Danube" in the Circus Episode is played in a minor key, and has a very melancholic tone.
This track from the soundtrack of Paprika.
The recurring number "Dream" from Mysterious Girlfriend X is definitely inspired by this.
In Dragon Ball Z several of Majin Buu's themes in the Funimation score have circus motifs, which totally fits the childishly deranged and pretty unsettlingly nature of the Manchild Humanoid Abomination.
A creepy little number called " Yuuenchi " plays in Cowboy Bebop when Spike Spiegel battles Mad Pierrot at his abandoned amusement park.
Sadly the OVA downplays this scene a lot and the creepy circus music is rather bland. The ringmaster believes it's a "march from another world", that the gas is sentient and is communicating and directing all the infected circus artists, since they move along with its rhythm. There's also an orchestra of infected monster clowns that play an eerie tune, and the ringmaster points out that they aren't playing the instruments, but only blowing the virus gas into them which comes out as otherworldly music on its own.
Gyo: Towards the end of the story, the main character stumbles into a Circus of Fear where the insane ringmaster is directing a show performed by infected people and animals.