Far Star Summer School: Emily, the youngest student at Sunny Summer School, puts up a front of acting like a Cheerful Child, but only because she hates feeling like her near-constant sadness makes her a burden. The dead look in her eyes when no one is looking at her hints towards depression.
Calliope from Homestuck acts very kind and cheerful, but inwardly she's depressed and for pretty good reasons ranging from body image and feelings of personal inadequacy to quite correctly fearing for her life at the hands of her sociopathic brother.
Aradia begins showing shades of Instability once she reaches god tier, and gets more unnerving in Act 6 Intermission 5.
She is not actually mentally unstable. She simply has an obsession with Time and death and sees it as something that one doesn't need to be sad about.
Daisy, a Newfoundland dog in Housepets!, can usually be seen with a gigantic smile and only saying "Hi, ImDaisy!" But when the K-9 Corps needs her help with Sasha, she drops her grin and explains that life may not always be very rosy for pet dogs.
Daisy: Sometimes it's easier to put on a happy face, you know?
Leez from Kubera is one. Despite her outward ditziness and cheerfulness, she's actually a Broken Bird after what happened to her village, and the events of the story don't help at all. Gods are generally the only ones who can notice this.
Erika in MegaTokyo, while currently a Deadpan Snarker as well as a badass Action Girl, was a voice actress and Idol Singer in her day, and still can't bear the thought of her fans thinking of her as anything but upbeat and bubbly. Dom calls her out on it by showing that even in the midst of a rampage of rabid fans and excessive taunting by him, she feels a need to keep her smile going.
My Deepest Secret: Emma keeps her worries and stresses inside, which leads to her eventually breaking down in front of Elios. Also, considering she's heavily implied to have a dark and troubled past, her behavior in general could easily be an example of this.
In The Non-Adventures of Wonderella Rita is tied up by a super-intelligent gorilla who boasts that his empathic helmet will give him the insight into humans he needs to take over. After hearing in a story in which her emotions fluctuate while she remains smiling, he's told that human ladies are supposed to keep smiling all the time, no matter how they feel. He responds by throwing away the helmet, and possibly giving up on wanting anything to do with humans.
In Sunstone Ally has aspects of this; she keeps her anxieties to herself to remain strong and at times forces smiles. Part of the story of the comic is Lisa gaining Ally's trust so that she can get to the 'human under the mask.'
Bastard: Jin, the main character, due to the double life he's forced to lead (as in, being an accomplice to his father's serial murders). He acknowledges that he's become a very convincing actor as a result.
Skids of Boy Meets Boy is mostly genuinely cheerful. But when things start to get him down, he simply pretends to be even more cheerful. This is extraordinarily creepy.
In Contest Jitters, Jerry clearly has issues with Janet's bodybuilding, but he hides them well enough for Janet to be oblivious to them.
In Evil Plan, it later hints that Computer ( Will) is both this and a Stepford Snarker. He cheerfully makes fun of Dr. Universe/Stan, and is usually pretty cheerful. Then you learn his tragic backstory and how much pain he had to go through. And then you see him crying behind a blue file with a smile emoji on it and your heart shatters.
In The Glass Scientists, Jekyll is the Depressed type. Outwardly, he's a polite, genteel socialite who always has a perfect smile for anyone and everyone likes him, but inside, he's a bundle of insecurities and self-loathing, always terrified that someone will discover the deception.
Lies Within: Lys is a cheerful, carefree guy whose Mental World, which represents all of a person's emotional connections, contains cracked theatre masks and nothing else. He eventually explains that he doesn't feel emotions strongly, isn't bothered by it, and only hides it to put other people at ease.
Desmond West in Monster Pulse. West's parents nominally accept him having an external and animate stomach, they treat it as a shameful nuisance and don't make any effort to accommodate his condition in their lives. But since he always tries to put a positive face on things and doesn't like to drag people down, the other kids don't have any idea how uncomfortable his life actually is and frequently scoff at him for not understanding them, not taking things seriously enough, and even of "not having real problems" like they do.
Paranatural: Cody, one of the more plot important side characters, is acknowledged in universe to often fake his smile. It's at least somewhat implied that he is attempting to become the mask or reject the influence of his inhumanfather.
The Archangel Michael from Satan and Me puts on a friendly/cheerful facade to get his way.
Torg in Sluggy Freelance is one in this strip, after beating the crap out of the psychiatrist and remembering he saw Zoe's unremovable cursed necklace at the scene of her supposed death.
Ollie Pompey of Something*Positive is, according to his uncle, "bottling it all up in a cask of finely-aged denial. His eventual breakdown will be my greatest artistic achievement". To what extent this is true is unclear, as Ollie was definitely performing Obfuscating Stupidity, but he is definitely in severe denial about how abusive his uncle really was, so he still has a dash of this.
Unsounded: Roger keeps up his foppish pretty boy act in public, but he's been having his mind and memories melted by Ruck for years to help Sonorie and when the attendants close the door he collapses to the floor. His mind is at its end and won't come back together after the next time Ruck envenoms him;
Ruck: Too much of my attention makes your minds grow so...brittle. He won't melt back together next time; not in the proper way. I love him so, but oh...oh well.
Mixed Gender Examples
Clarissa's family from the Clarissa comic series. Her mother tries to play a perfect 50s-style housewife, but blames Clarissa for her own molestation and wants her to just "admit" it's all her fault and pretend nothing's wrong, trying to bribe her into "behaving" with gifts and toys. Her father plays "perfect dad" while molesting Clarissa and manages to be insulted that she's terrified of him and can't see him without vomiting. One of her brothers is a neurotic mess that tries to pretend everything is normal in hopes that wishing it hard enough will make it so. Her other brother presents the image of the clean-cut, perfect son, but bullies and taunts Clarissa for daring to be traumatized by her experiences and "ruining things" by being a victim of molestation. The comic is the blackest of Black Comedy, finding humor in this ugly situation which is reality for too many children without pretending that it isn't truly horrible and vile.
This is very prevalent among the depressed characters in Depression Comix, and is represented by a character holding a card with a large smile drawn on it over their mouth.
Dani tries to be a happy, cheerful girl, but it's clear nearly being burned at the stake and seeing a friend murdered shook her more than she wanted to admit. After thinking she saw her brother Dorian burned at the stake, she finally breaks.
Nico is a joker who seems to be a happy person. Secretly, he wants to be a witch and feels abandoned, especially by his adoptive father.
The Order of the Stick give us the Empire of Blood, an entire nation that smiles and steps ultra carefully because committing any minor crime or act of rebellion will result in them being packed off to the Gladiator Games, eaten by a dragon, or worse. Best exemplified in this strip, where a pair of reporters are covering a parade held in the Empire. Within seconds of the female reporter accurately identifying a group of marchers as the Empire's death squad and criticizing the regime, she is shot with a poisoned arrow and replaced by a female member of the death squad. All the while, the male reporter keeps smiling.