Robot 13 from Gunnerkrigg Court is remarkably easy-going about his own well-being, taking the loss of his arm (and later, the loss of everything except his CPU) in stride. On the other hand, he becomes very distraught upon thinking that he hurt his "Mommy", Antimony.
Joyce of Roomies / It's Walky! took being a Pollyanna to new levels; Ignoring and/or avoiding anything that would put a dent in her rose-colored worldview (To the point where merely being forced to watch porn could break her mind. The argument could be made that Joyce wasn't a true Pollyanna as much as she was a different flavor of Love Freak.
Played with in Dominic Deegan. Gregory is probably the most cheerful person in the cast, despite the sheer amount of crap he's been through. But when he starts to form a new band, his soon-to-be bandmates call him out on this, and he lists some of the things he's been through. His bandmates are speechless.
Tavros from Homestuck. His life is pretty horrible all around, since he can't walk, his horns make it hard for him to sleep, his beloved Lusus (basically a cross between a parent and a pet) dies and the nicest thing anyone has done for him in the comic is cutting off his legs with a chainsaw so he can get a robotic pair. He's pretty happy despite all of this.
John, just... John.
EB: well to be honest, i never really believed any of your guys's doom and gloom nonsense.
EB: not because i think you are lying...
EB: i just feel like there must still be a way to win!
AG: That's the spirit, John!
AG: That is a winner's attitude, and there is always hope for someone who has that.
EB: yes, i agree.
EB: also, there is always hope for someone who has good friends to count on!
Even in the Post-Scratch universe, where he was raised by Betty Crocker/the Condesce. He even grew up to become a famous comedian.
Feferi. Not even being dead can diminish her spirit. Her friend Sollux (during one of his pessimistic phases) described her as "so ridiculously optimistic it's kind of sickening".
Oddly enough, Aradia. She starts off as an Emotionless Girl, but when she does regain the ability to feel, she becomes enthusiastically cheerful and smiles almost all the time. Even as her friends fight off killers in their midst, and she faces a near-omnipotent monster, she's convinced that there's no reason to grieve and that everything will turn out fine.
Alice, The Medic from Dead Winter. You do see her get upset once in a while (for instance, when Trenton died), but she's the type to move on from bad things since being sad is just a distraction from her main drive, which is to help others.
Buwaro from Slightly Damned. His parents were killed before he was born, he was injured whilst in his egg and was born perpetually insane, and the only thing stopping that insanity is the pendant he always wears, he was abandoned alone in the Ring of the Slightly Damned for years, his sister was killed in their escape from hell, most people on Medius will try to attack him on sight and as a demon he doesn't get an afterlife. Despite this, he's still a loving goofball.
Of course, there's evidence that he wasn't just born insane, but also retarded. Leo retarded. His favorite game is throwing a large rock up and trying to catch it. It works out about as well as you'd expect, but he's still always cheerful.
The titular character in Equinox: Defender of The Horde. He is a silly Man Child who seems to see the world as a cartoony adventure. But throughout the story he faces death, betrayal, treason, and heartbreak, and while shaken to the bone at times with his experiences, he nonetheless manages to keep his optimistic childishness.
El Goonish Shive: Grace suffered years of trauma at the hands of Damien before being introduced. Although she reacted as anyone else would when it caught up with her, she has since become the most upbeat, positive character in the comic. However, this is strongly implied to be a facade; she's still a wreck underneath, and it sometimes shows.
Precocious: Max and Ursula both, although Max isn't completely oblivious.
Max:[to Ursula] Not all of them are nice all the time.
Mia of True Villains is cheery and bright no matter what befalls her.She had an exceedingly rough life before joining the team, and even when faced with death, monsters, and amazingly powerful magic, she keeps a smile.