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.
Grace from El Goonish Shive seems to be veering into Depressed territory, with occasional powerful beings advising some help before she pops on over to Unstable.
Shroomy from Electric Wonderland has a cheery and naive demeanor undermined by depression caused from continuously crushed hopes.
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.'
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.
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.
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.
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.
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.
The Archangel Michael from Satan and Me puts on a friendly/cheerful facade to get his way.
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.
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.
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.
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.