Conor Oberst’s “Danny Callahan” is very peppy. It took me a couple of listens before I paid enough attemtion to the lyrics to notice that it’s about a little boy who dies from leukemia.
“Girlfriend in Coma” by The Smiths
“. . . there were times when I could have murdered her but you know I would hate anything to happen to her. No, I don’t want to see her”
Oingo Boingo also has lots of songs that fit the criteria
“Little Girls” as song from the viewpoint of a pedophile is about the peppiest, poppiest ,happiest tune I can think of
“I love little girls they make me feel so good.
I love little girls they make me feel so bad
When they’re around they make me feel like I’m the only gut in town”
Another incredibly dancible tune with a molestation motif is “Elevator Man”
“…please pretty baby won’t you come to me
won’t you let me be your daddy come sit here on my knee
tell your sugar daddy all of your fears
cry for me darling let me taste your tears”
My Sharona probably fits in this category although they leave her age a “mystery”.
Oh, yes. TMBG also does songs about heads. And beheadings. And skulls. And decapitation. And slow removal of parts of presidential heads (and the last one is supposed to be a children’s song). 
Jonathan Coulton’s songs often have what could be disturbing subject matter, but he’s more the Terry Pratchett of pop music, whereas TMBG is sort of a Neil Gaiman/ Douglas Adams hybrid. Coulton goes for a combination of the laugh and the “awww,” and mines traditionally “dark” subjects for both - often by finding ways to humanize otherwise inhuman characters. TMBG/Gaiman/Adams on the other hand, use traditionally “happy” means to tell very dark stories.
IOW, Coulton’s approach is an inversion of TMBG’s to some extent. He writes “ack gross… aw, wait, that’s actually kinda cute” rather than the “hahaha… wait, that’s actually really depressing.”
Natalie Merchant - What’s the Matter Here:
“We live on Morgan Street;
just ten feet between and his mother, I never see her,
but her screams and cussing, I hear them every day.
Threats like: “If you don’t mind I will beat on your behind,”
“Slap you, slap you silly.”
made me say, “O, what’s the matter here?”
I’m tired of the excuses everybody uses, he’s your kid, do as you see fit,
but get this through that I don’t approve of what you did to you own flesh and blood.”
A lot of her songs are like that - if you don’t listen to the words, they sound really upbeat and happy.
The classic Irish band staple Whiskey in the Jar, which is about murder and betrayal.
And I think I remember Bobby McFerrin saying in an interview that he didn’t understand why Don’t Worry, Be Happy was seen as such a positive song, because it was about a guy whose life is falling apart and he’s just smiling away instead of doing anything about it. Could have hallucinated that, though.
I’ll agree that it’s dark but I’m at a loss as to how anyone could think it sounds happy.
Three pages and no “Novocaine for the Soul” yet?
Come to think of it, Tom Jones’s She’s a Lady qualifies. It is so catchy and fun, but the lyrics are largely repulsive misogyny.
Jonathan Coultan is pretty good at this.
Code Monkey, The Future Soon, Still Alive
Also the Irish excel at this sport.
Molly Malone, The Irish Rover, Sally MacLennane
The Rolling Stones - Brown Sugar
Yeah, I guess I was purely thinking of the music, and not the lyrics.:smack:
Richard and Linda Thompson, “Wall of Death”
Tom Jones’ “Green Green Grass of Home” seems pretty peppy, until you realize it’s about a prisoner facing his execution.
Lots of novelty songs use this technique for comic effect. Weird Al’s “Happy Birthday” and “Christmas at Ground Zero” come to mind, as does The Beat Farmers’ “Happy Boy.”
Nobody’s mentioned “Beyond the Sea?” Sounds like a crooner love song, but the lyrics speak of a near-suicidal longing for death.
Huh? They speak of wanting to be reunited with a lover across the sea. It’s about as suicidal as “My Bonny Lies Over the Ocean”.
My little dog spot got hit by a car
Hubba hubba hubba hubba hubba
Put his guts in a box and put him in a drawer
Hubba hubba hubba hubba hubba
I’m a happy boy (Happy Boy)
I’m a happy boy (Happy Boy)
Oh, ain’t it good when things are goin’ your way, Hey Hey!
Love that song!
Yeah…take another glance at those lyrics. 
It’s a little bit subtle, but the lover in question is dead. She’s waiting on the shores of Heaven.
“It’s far beyond the stars
it’s near beyond the moon
I know beyond a doubt
my heart will lead me there soon”
The singer is waiting for death to carry him “beyond the sea” where they’ll be reunited and he’ll leave “never again.”
If you try to interpret the lyrics as “she’s across the ocean,” the phrasing is very strange and the lyrics of the bridge are completely indecipherable.
“The Future’s So Bright, I Gotta Wear Shades”–a song about nuclear war