Chandelier by Sia.
From Wikipedia: “Lyrically, the song has a melancholic theme, detailing the demoralisation and rationalisation of alcoholism through the typical thought process of a “party girl”.”
As far as pop songs go, I love it.
Joni Mitchell’s Big Yellow Taxi
Adam Duritz of Counting Crows sang it, too, but didn’t know enough to rhyme “see 'em” with “museum”, preferring to sing “see them”. Probably things like that made his girl leave him.
Foster The People’s song Pumped Up Kicks seems pleasant and relaxing till you realize it’s the homicidal thoughts of a kid who found his dad’s gun.
What could be more light hearted and innocent than a children’s song?
Ring-a-round the rosie,
A pocket full of posies,
Ashes! Ashes!
We all fall down.
The fact is, however, that there are eerie similarities between the rhyme’s lyrics and the circumstances surrounding the deadly plague that swept across Europe and killed many millions of people. The theory is that the “ring-a-round the rosie” referred to a red circular rash common in some forms of plague. The posies would have represented the different flowers and herbs people carried to ward off disease. The "ashes” and falling down was supposed to mimic sneezing and eventually dying from the disease.
This theory is not universally accepted, however.
Maxwell Edison, the beatles.
ETA the name of the song is ‘Maxwell’s Silver Hammer’
First thing that came to mind. Quite a few of the Smiths are bouncy and happy until you pay attention to the lyrics but I think this one may be the peppiest / darkest of them.
Easily half of Oingo Boingo’s catalogue fits the description; one of my favorites is a perky little number sung from the point of view of a paedophile called Little Girls 
I dare you to listen to that and not dance.
And Sefton, do you maybe actually mean **Third Eye Blind’**s Jumper?
*Pulaski *- Drive-By Truckers Pulaski by Drive-By Truckers - YouTube
Jaunty little ditty about a nice country girl who moves to California and ends up coming home in a box.
Six O’clock News - Kathleen Edwards Kathleen Edwards - Six O'Clock News - YouTube
Lovely tune about Suicide By Cop.
Let’s go way back - look at the Supremes smiling and dancing to this happy tune, then listen to the lyrics. :eek: 
One of the strongest contenders in the category (in my opinion) - Ruby, Don’t Take Your Love To Town. So peppy, with that tootling little guitar going on! “If I could move, I’d get my gun and put her in the ground…” :eek:
You just reminded me of The Fratelli’s, “Everybody Knows You Cried Last Night”
Uh oh…looks like I have a new hobby. Touches the ear a bit like Black Parade, and that’s always a good thing. Thanks for this.
A lot of songwriters just seem afraid of writing slow gloomy music to fit their lyrics.
Maybe they’ve heard that slow & gloomy doesn’t sell. But if you’re writing about sad stuff, it’s weird to add peppy music - unless it’s intentionally ironic.
Maybe they all watched Dr. Phil - “Do you want to be right, or do you want to sell recordings?” 
Or maybe slow songs would show off how bad their band really is.
I don’t understand your point. “Music Up, Lyrics Down” is an old, time-honored approach to songwriting. Gloomy lyrics sell just fine.
I’m lamenting the lack of “Music Down, Lyrics Down”.
Pop Music tends to not be Music Down. There are love ballads, and Torch songs (I Will Always Love You as interpreted by Whitney, some Adele, etc.), but Pop songs tend to have a little…pop to them 
One Time One Night–Los Lobos
Yup. I start to think “Sad Songs That Actually Are Sad” would be the harder more interesting thread, and that the answer to this thread is “well, most of them actually.”
A happy little song about apathy: Outside of a Small Circle of Friends– Phil Ochs
“Beer for My Horses” is about lynching.
Clarification: It’s from the lynchers’ point of view.
Cecilia by Simon and Garfunkel. This woman is freaking cheating on you… and you’re happy she’s back?
While I’m on Paul Simon… You Can Call Me Al. This man has clearly lost someone important (“now that my role model is gone.”) and is trying to fill a gap in his middle-aged life. He’s so alone.
And one of my least favorite songs (because of the lyrics)… Escape (aka the Pina Colada song). This man is so freaking unhappy in his relationship that he’s looking through the personals for a new girl… and picks one. He meets up with her, fully intent on cheating or running away from his long-time love. Then he finds out the woman whose personal he responded to is actually his woman. She’s unhappy, too! But instead of dealing with the issues that lead them to seek affairs, they shrug it off as a fun coincidence. There are some deep issues in that relationship, but, hey. Let’s drink pina coladas instead.