Wolverine (Red Oni) and Cyclops (Blue Oni) - Wolverine's color may be yellow, but he's easily the Red Oni of the team.
From Everywhere in ElfQuest: there's Cutter and Rayek, Two-Edge and Winnowill, Ember and Suntop, and Bearclaw and Joyleaf.
During the Dork Age when Superman was an energy being, he was briefly split into two separate characters, the calm and rational Superman-Blue and the hotheaded Superman-Red. This was actually inspired by a classic Silver Age Imaginary Story — though in that, both Supermen were more or less the same.
Green Lantern: Hal Jordan and Guy Gardner are Red Onis; Kyle Rayner and John Stewart are Blue. There's usually at least one pair of them working together, and they make this trope.
An "emotional spectrum" has been established in recent years, explaining that each major emotion has a color associated with it: Lantern Corps using the "warmer" colors are unrestrained and selfish Red Oni (red rage, orange greed, and yellow fear) while the "cooler" ones are calm and focused on others as Blue Oni (blue hope, and indigo compassion). The exception are the Star Sapphires who wield violet love, as their color is one of the "cooler" ones but they're easily as passionate as the "warm" Corps.
In a more literal color contrast, the power of Blue Lantern corps can neutralize the effects of a Red Lantern Ring of Power in its user, both the emotional (mindless rage) and the physical ones (severe weakening of the original circulatory system, as the red rings replace this body function).
Sort of a running theme with Deadpool, actually. Another example of a Blue Oni paired up with him is Taskmaster, a level-headed mercenary whose unique abilities are based around observation and analysis and who will typically run away from a fight if he determines that he can't win it, in contrast with Deadpool's typically cheerful, brainless recklessness, but the most striking comparison is probably with Domino, who, like Deadpool, is the cast-off product of a secret government Super Soldier program and favours the same style of costume and equipment (even wearing what was essentially a blue-and-black woman's version of Deadpool's distinctive red-and-black bodysuit in the Cable & Deadpool series), but is typically cold, clinically rational, and often emotionally conflicted over her actions, and her special ability is essentially not getting hit at all in a fight, where Deadpool's powers effectively allow him to wade anything that's thrown at him.
Comes up again in Uncanny X-Force with Fantomex, the cool and calculating gunslinger whose powers let him manipulate his enemies into fighting each other. And, as with Cable, Taskmaster, and Domino, they are (sort of) friends.
Saxon and Kenzie from Mouse Guard—even their cloaks match.
Hawk and Dove of DC Comics are an embodiment of this trope, with Hawk being red and Dove being blue. Hawk is an aggressive muscleman, quick to anger and always ready for a fight. Dove is a cool, slender peacekeeper who tries to avoid direct conflict whenever (and however) possible.
Fire and Ice seem to fit this one, although the red oni is dressed in GREEN!
You could make a good argument for Batman (the cool, calculating Blue Oni) and Robin (the more impulsive Red Oni). Batman is also a Blue Oni to The Joker's Red Oni.
This is reversed in Grant Morrison's Batman, where original Robin Dick Grayson takes over the role of Batman, while Batman's son Damien becomes Robin. Dick is cheerful and spirited, Damien is somber and brooding. This also mirrors the dynamic between Dick-as-Nightwing and both Nite-Wing and the Red Hood.
The most definitive Batfamily example would be Tim Drake(blue) and Stephanie Brown(red).
In Batman-Superman team-ups, usually the writers emphasize Supes' Red Oni qualities and Batman's Blue Oni qualities, even matching their cape colors. Likewise, when they team up, Lex Luthor has his Blue Oni qualities emphasized and the Joker his Red Oni ones, though their color schemes tend towards the purple and green. However, when the Joker makes an appearance with Harley Quinn, he becomes more of a sociopathic Blue to balance her Red.
Gemini Storm has Elizabeth, who is cold and snarky, and Midnight, who is more prone to outbursts. In battle, though, the moods switch. Midnight calculates every move, whereas Elizabeth is much more...enthusiastic.
Sin City has two assassins working for the same organization: Blue Eyes and Mariah. As expected, Blue Eyes has blue eyes and wears blue (she's one of the few characters in Sin City that has color added). Likewise, Mariah is also one of the few characters in the series that isn't Deliberately Monochrome. She has bright red hair and wears red spandex. Blue Eyes is the Black Widow, seducing men and killing them quietly. Mariah is verbose and prefers just to chop people up when she kills them. While we never actually see them together, they do reference one another and have the typical "Red vs. Blue" rivalry.
Dwight, normally a pretty calm guy, has had two red onis to his blue oni. He usually teams up with Miho, who is much more violent and probably a little unbalanced. He has employed the help of Marv as well, resulting in a similar relationship.
The title character of Shakara has full red eyes and is, in fact, a completely red liquid being in a suit of powered armour; he is also insane, reckless, and driven exclusively by rage and hatred. This stands in stark contrast to Cinnibar Brenneka, hero of the Shakara, who was always very stoic, rational, and driven by a higher calling. He also had blue yes and body markings.
Augustus and Julius Furst, patriarchs of the Furst Family in Astro City. Augustus is a dignified, spare man, who can calculate anything to the sixth decimal in his head and rejigger any Phlebotinum needed to save the day in minutes while puffing on his pipe. Julius is a shaved-headed Boisterous Bruiser who spends his free time knocking back Budweisers and arm-wrestling. When evil-doers show up, Julius chomps down on a cigar, picks up his BFG and wades into the thick of it alongside his super-powered niece and nephew.
May can also be seen as the Red to Darkdevil's Blue thanks to their CousinYinYang.
Raphael and Leonardo of TMNT are Red and Blue oni respectively: Leonardo is the calm, thoughtful, and self-controlled leader of the team, when Raphael is the easily-angered, hot-tempered rebel. It's even lampshaded by their bandanas.
Danael and Gryf from Les Légendaires. Danael is a usually calm and collected paladin who likes controlling events, tends to plan everything before battle and had apparently difficulty confessing his feeling toJadina(though, eventually, he did). He means the right thing, but will occasionnally be ready to go to extreme measures for the greater good and act like a borderline Well-Intentioned Extremist. Gryf, on the other hand, is a Book Dumb, Anti-Hero who has no problem doing things like cheating at games, is described as the bravest of the Legendaries, and usually lets his emotions and instinct lead him, but is notably more relaxing than Danael. Both are still best friends, however.
While Lady Death was part of Chaos Comics, she was the cold, sinister Blue oni to the feisty, bloodthirsty Red oni of Purgatori!
Harvey Dent and Two-Face are this in one body, by some interpretations. Harvey Dent is the calm, rational side, while Two-Face is more often than not just portrayed as unrestrained rage and hatred.
Sonic The Comic Sonic and Shortfuse are the Red onis to Amy's and Tekno's Blue onis also there is The Badnik Army Repair Functionaries (or B.A.R.F.) which has Bert a Red oni and Cam a Blue oni.