“Santeria” by Sublime and “Semi-Charmed Life” by Third Eye Blind are two such examples.
What are some other ones?
Pearl Jam’s “Jeremy” (about a school shooting) is one of their more upbeat songs.
Ring Around The Rosie
“Hey Ya” is a very danceable song. I didn’t realize how depressing it was until I heard an acoustic cover of it.
“Pumped up Kicks” by Foster the People.
Almost everything by Scissor Sisters. I especially enjoy their cover of “Comfortably Numb.” A couple others I rotate often are “I Don’t Feel Like Dancin’,” “Baby Come Home,” and “Take Your Mama.”
You think hearing “Jeremy’s broken” over and over is upbeat?
Jonathan Coultan has many songs like this. One of my favs is Betty and Me about a guy who is so excited that his girlfriend (wife?) is having a baby but if you listen to the lyrics you understand that he is not the father.
Lyle Lovett’s LA County.
I don’t think most people knew what it was about until some media outlet picked up on it. It was in heavy rotation long before there was a Cracked or Buzzfeed to explain it to us (and a FB to perpetuate it) and IIRC the original video got edited either very quickly or never aired with the suicide being shown. At some point, (I’m going to say at least a year after it’s release) you started hearing that it was a true story about a kid killing himself in school. But most people don’t listen to lyrics and even if they did, Eddie does have a habit of mumbling a bit.
Look at Semi-Charmed Life that someone mentioned upthread. That song used to be on every Top40 station at least 10 times a day. It’s about doing meth and having sex, but even if you don’t pick up on that, the lyrics pretty clearly infer cocaine use, but we all sang along to the chorus, we just missed the rest of it (even though it’s mentioned in the chorus as well).
You mean “Jeremy spoke in”, right?
“Bonnie Mae” is a bright, lively, springy song by the Irish-American band Solas. It’s about the rape of a shepherd girl by a lord.
Isn’t it ‘Jeremy’s spoken’?
I can’t find anything that actually has that listed…
I saw the “Jeremy” video all over MTV when it was first released. It was very clear.
When I saw the title, first song that came to mind was “semi-charmed life,” as mentioned in OP. I can’t think of a more definitive example, for me.
No, it’s “Jeremy’s pokin’…classss todayyyyl.” He’s poking the class.
Isn’t Alone Again the ultimate example of this?
Janie’s Got a Gun by Aerosmith
REM’s “The One I Love”- a shallow view of the song might make you think it is a traditional love song-it most certainly isn’t…
Vou festejar, a samba song.
With lyrics like “Cry, I don’t care!”, “It’s your time to pay me back!”, “You betrayed those who helped you”, and “I’m going to celebrate your misery and suffering!”. 
Ah!
Cherry Hill Park by Billy Joe Royal. A peppy little ditty about a girl who regularly “plays games way after dark” with “all the guys”. Yes, she is happily, voluntarily gang-banged by all the guys in the neighborhood until she is ‘bought’ by a guy with money. The singer is sad this disturbed young woman isn’t around to service them any more, and is disappointed that she’d stop giving it away for free - but would stoop to taking up with “a guy with money”. A girl who probably was severely sexually abused as a child and is acting out has the nerve to leave them, to become a paid whore! The nerve!
That’s pretty much the formula for “thoughtful” hit songs - music Up, lyrics Down.
John Lennon/The Beatles - Help, I’m a Loser
The Police - lord, Sting’s entire body of work - King of Pain, Man in a Suitcase, There’s a Hole in My Life, Message in a Bottle…