Mary Marvel was described as this during her pre-Countdown and Final Crisis portrayals. This was her most obvious comedic trait in the Superbuddies stories. She is also explicitly called "Pollyanna", causing her to talk about how that's her favorite movie.
Billy himself used to be a pretty good example of this as well (before the New 52 changed everything). By the time he's an orphan, has endured abusive foster parents and lives on the street, but he somehow manages to be one of the most Cheerful Children in the DC Universe. Admittedly a lot of his problems were able to be solved once he got super powers.
In the New 52, the Pollyanna status seems to have been taken by Billy's foster sister Darla. At first energetic about having another older brother, Billy later coldly tells her that he is not her brother and her other siblings are not an actual family because they aren't related, which drove Darla away in tears. Mary coldly tried to put Billy in his place for what he did, saying Darla was with them simply because her Jerkass biological parents didn't want her and told her exactly that to her face. The next morning, however, Darla acts as if the previous day didn't happen. Mary mentions it's because Darla doesn't waste time on anger.
M'gann M'orzz aka Miss Martian, despite her White Martian heritage (White Martians tend to be vicious warmongers), is an absolutely adorable Pollyanna. Almost nothing gets her down — her response to tragedies such as murdered parents, an evil future version of herself stuck in her head, the deaths of teammates, and nearly being killed herself on several occasions, is to think positive and work for a better tomorrow.
Superman may also qualify, although the amount of crap in his life (and therefore the strangeness of his constant kindness and optimism) varies from writer to writer, and era to era. However he unfailingly believes in the goodness of the human race, and frequently bucks up other superheroes by promising that no matter how bleak a crisis looks, they can always do something to help. Like Apollo, he is powered by the fucking sun, thriving on light and warmth, and it sure as hell suits him.
The Blue Lantern Corps, representing the blue light of hope, always hope for the best in even the worst situations.
Stephanie Brown, Spoiler, who is also known as the fourth Robin and later on the third Batgirl. She has had an emotionally-abusive, villainous father; a drug-addict mother who left her alone during her childhood; a jerkish ex-boyfriend who got her pregnant; a rocky relationship with Tim Drake, the 3rd Robin; not getting approval from Batman and the Birds of Prey; getting tortured by Black Mask and her controversial 'death' (retconned later to her just fleeing the country with Leslie Thompkins); then coming back to Gotham only to be rejected again by Tim Drake — it's a wonder how she managed to keep her sunny disposition and not get boggled down with angst. She is the most hopeful and lighthearted of all the Batfamily members.