The British airmen from 'Allo 'Allo! remain upbeat no matter how many times their attempts to get home are foiled.
Basi from the Nigerian TV show Basi And Company is remarkably cheerful for a broke, unemployed (and unemployable) man living in a one-room apartment (which he insists on calling "Basi's Palace"). Basi's landlady wants him out, but he's so sunny that nothing she does, including taking his only mattress, can get him to leave.
Budoy, from the 2011 Filipino drama of the same name, is an interesting Rare Male Example. Interesting in that, while he does have the sunny disposition of the Pollyanna, this one might actually be partly due to the fact that he is diagnosed with Angelman Syndrome, a mental disorder that does create the happy and childish personality that he exhibits. Even in the finale, he still is a Pollyanna.
The ditzy Nymphs from the Charmed episode; "Nymphs Just Wanna Have Fun".
Annie in Community. Pollyanna was even used as a nickname by Jeff, when Annie's attempt to help Pierce with his ex-step-daughter backfires.
Control Z: Rosita, the most cheerful and actively extroverted student of the popular clique.
Dr. Quinn, Medicine Woman's sister Rebecca is this, though after a confrontation with her conversely depressed sister Marjorie, she confesses to Mike that although she's not secretly unhappy, it's sometimes exhausting to be cheerful all the time and unfair that she doesn't get to admit it whenever she is sad.
Friends: Phoebe's boyfriend Parker (Alec Baldwin), who annoys the rest of the gang and eventually Phoebe herself with his constant cheerfulness about everything.
Parker: Im sorry thats who I am. Im a positive person. Phoebe: No! I am a positive person. You are like Santa Claus on Prozac, at Disneyland, getting laid!
Ted from How I Met Your Mother, whose unwavering (and often irrational) amount of optimism and belief in love and friendship persists through a ridiculous amount of cynicism-inducing crap. Especially true in the field of romance, including a high school girlfriend who abandoned him immediately after tricking him into giving up his virginity for her, a college girlfriend who cheated on him constantly, having to break up with Robin even though he was in love with her, and a fiancee who left him at the altar. Oh, and he fully believed he could make it rain through The Power of Love, and succeeded. When he finally expresses a measure of pessimism in the season 7 premiere, it's a pretty disquieting moment.
Kamen Rider Den-O: Nogami Airi (the main hero's sister) suffers from selective amnesia. Apparently it has the side-effect of leaving her in a permanent state of semi-creepy, almost Rain Man-like cheerfulness.
George the Loner (played by Mark McKinney) in a The Kids in the Hall sketch. He's always smiling despite the fact that he doesn't have any friends and he often gets drunk. When he stubbed his toe and no one told him to go to the hospital, which resulted in his toe becoming infected and his leg going numb.
Parodied in a skit of Key & Peele where two prisoners of a psycho clown are so optimistic, they end up driving the clown insane with frustration at not breaking their spirits.
In Lodge 49, Sean Dudley has, in the space of only a year or so, lost his father, his childhood home, and his business, and suffered a Dream-Crushing Handicap that has left him in debt up to his eyeballs. Despite this, he is relentlessly optimistic.
Mara David, from the Filipino soap Mara Clara definitely fits into this to a T. In fact, she can be considered as the single biggest reason why this trope has become a staple of Pinoy teleseryes. While the girl does cry buckets, she can still remain happy even with all the torment that Clara (the second titular character) throws at her. Even when it was revealed that she and Clara were switched at birth, Mara still has her sunny disposition intact.
Subverted in the 2011 remake of the series. Mara actually does break (and occasionally snaps), becoming more cynical in the latter part of the story.
The teacher in the Mr. Show sketch "The Chip-on-the-Shoulder Club." All the kids are jaded and none of them want to be there, but the teacher is still determined to get the students to be motivated about something (school, their future) even when all of them are jerkasses to him.
Erin on The Office (US). She's Pam's replacement as receptionist at Dunder Mifflin. She's more upbeat and cheerful than her co-workers and actually seems to enjoy working for Michael (but it could be because she's new). She somehow manages to find the positive in Michael lying to a group of underprivileged teens about paying their college tuitions in "Scott's Tots". We also learn in "Koi Pond" that she's an orphan.
Leslie Knope. She is always smiling despite the fact that she lives in an insane town that hates everything she does and is surrounded by cynical government employees. She loves her town, her coworkers, and her job, and often manages to force good deeds through the government by sheer perseverance. Even her boss, Ron Swanson, who hates absolutely everything she stands for, respects her unwavering dedication.
Mark: It took two months for this job to crush my enthusiasm. Leslie's been here for six years and is still going strong.
Chris Traeger makes Leslie look like a suicidal emo teenager. He is a chirpy health food nut who has two moods: Happy, and super happy. He loves everyone he meets, learns their names and likes and habits, and helps them with anything he can, whenever he can. Although some people find him disquieting to be around, no one ever doubts his honest and earnest dedication to helping people.
Chris: When I was born, the doctors diagnosed me with a blood disorder and told my parents I had three weeks to live. Now here I am, some two thousand odd weeks later, and I have enjoyed every single one of them.
There was a 1989 made-for-TV Race Lifted (black) remake of Pollyanna, called Polly. Near the climax, the main character falls out of a tree, is seriously hurt, and is morose from there on out. By this point, she's cheered the town up so much that they try and get her to cheer up, by creating a "Polly Day". It works. Something very similar to that happens in the original story, too.
Dr. Molly Clock (Heather Graham) Drs. Cox and Kelso decide to teach her that we live in a World Half Empty. It doesn't work.
Sonja "Sunny" Dey in season 8, who at one point tells the Janitor that she has to be strong to always be smiling on the outside when sometimes she's not smiling quite as much on the inside.
Jared from Silicon Valley. Over the course of the series he's stuck on an uninhabited island full of robot forklifts, kicked out of his home by an asshole tenant, and forced to sleep in a rat-infested garage, all while maintaining an insanely positive attitude. And that's nothing compared to his childhood.
Kimmy in Unbreakable Kimmy Schmidt: Kidnapped by a cult and kept in a hole for decades, but due to having experienced the most horrible thing that would ever happen to her she remains relentlessly cheery about everything else.
Vagrant Queen: Amae keeps her optimism no matter how bad things appear.
The Wilds: Shelby is described this way, and at first it fits her as she's aggressively upbeat, maintaining her optimism despite the circumstances. However, it turns out she's nursing some serious issues. After they come out, she gets very depressed, before mellowing on resolving them somewhat.