The Guild: Clara's smiling, friendly demeanor hides a criminally neglectful mother and a treacherous backstabber who creates an alternate character to attack Vork and makes out with a man Codex is interested in.
In Funny Business, it is eventually revealed that Jeannette is actually self-loathing and has a massive Guilt Complex, and is only pretending to be a Cheerful Child so that her loved ones don't worry about her.
Pyrrha Nikos is a downplayed example. While she is a genuinely sweet girl who is grateful for her incredible talent, she feels isolated from people for so long because nobody sees themselves as good enough to be around her.
Emma Approved: Emma Woodhouse, who acts confident to a point of arrogance despite several cracks that show how little self-esteem she actually has.
Twig: Helen, an Artificial Human with emotions disconnected from her physical reactions. She can play at any given role, but beneath whichever face she's wearing that day is an emotionless blank with inhuman predatory instincts.
Pinkie Pie had a very subpar fillyhood full of emotional abuse at an orphanage due to being both an Earth pony and Romani. As an adult she uses a very cheery persona to hide her problems, with it rarely cracking even when singing depressing but chipper songs
Rarity and Applejack are both Shellshocked Veterans, though Rarity is more-so. Rarity is trying to recover but it's obvious the trauma has taken a toll on her. Applejack on the other hand seems to be ignoring her issues and acts like a war hero, despite her numerous war crimes and the things she saw.
Red vs. Blue's Dr. Emily Grey is a bit too maniacally cheerful for someone whose planet is locked in a never ending civil. The Ultimate Fanbook confirms that, surrounded by death 24/7, she put on a "Happy Face" so much that eventually she suffered from Sanity Slippage, Became The Mask, and hasn't taken it off since then.
Like the The Nostalgia Chick, The Nostalgia Critic also delves into this on occasion. Mostly when a movie does something good then completely fucks it up but also when he was talking about his parents.
*shows a picture of his kindergarten self being ripped apart by two monsters labeled "Mom" and "Dad"*
Kid-friendly version with Tom from The Cartoon Show, who tries his hardest to be polite, but represses an unhealthy amount and only just barely manages to hide his frustration.
Yandere High School reveals that Sam is violent and mentally unstable without Taurtis. To cope, he tries to force Grian to replace Taurtis, but the absence of his best friend and Yuki's psychotic nature drive him crazy.
Mixed Gender Examples
Quite a few of these have shown up in Survival of the Fittest, surprisingly. Most of these tend to be Depressed, for obvious reasons. Some examples:
Former gamer Warren Pace gives himself a complete image makeover to fit in with the football team due to his perceived images of jocks.
Maria Graham has a bad habit of burying any pain and angst underneath an overly cheerful, energetic persona. It's already been shown before that when she finally crashes, she crashes HARD.
She ended up crashing pretty early once the game started, though she often tries to put it back up again. Eventually she succeeds when Duncan McMahon, her childhood friend and love interest dies right in front of her, causing her to finally lose her mind.
Hermione Miller also has been shown to have tendencies of this. She spends most of her run in serious denial, believing that she is at the campsite while acting eerily cheerful and rejecting all signs that she's stuck on a Deserted Island. Eventually she has a revelation about her situation and that no one will take her seriously due to her being The Ditz, and right after is Driven to Suicide. She also receives a fair amount of Lampshade Hanging comparing her to the Trope Namer.
In mini site Spin-OffThe Program, Brigadier General David Adams, the founder of the title game, is very possibly) Unstable. He has been described as pretty casual looking for a military organization, and oftentimes slides into Cloudcuckoolander mode during announcements. However, he has shown to have a very chilling approach towards the idea of children killing each other, and seems to really be enthused by it. Needless to say, there's a lot of Dissonant Serenity in his announcements.
The Whites from Lucky Day Forever can be seen as Empty. They are always shown donning a smile on their faces, as if it's the only expression they wear. The only thing they managed to do is to trick the Proles into becoming their Human Resources.
Put the paper away, it's time to eat, Justin thought. Yes dear. Mmm. Smells delicious.
"Put the paper away, it's time to eat," Dorothy said. She was holding the coffee pot, stepped behind Geoff, putting a hand on his shoulder, and bent down to kiss him on the top of his head. Automatic, without affection.
"Yes, dear." Geoff said, smiling up at his wife. "Mmm. Smells delicious."
From Welcome to Night Vale: Literally all of the town Desert Bluffs, run by the evil corporation StrexCorp. In particular, the radio host Kevin, who on the whole is much cheerier than our usual Cecil, but reportedly doesn't smile right. Also, his studio is covered in blood and viscera.