Dream of the Endless in "The Sandman" is blue oni (the kind with lots of inner turmoil) next to virtually everyone he encounters. Most notably he plays the role throughout his relationships with his ever-cheerful and sociable sister Death and with his rambunctious brother Destruction. In Brief Lives in particular he plays blue to the red of his sister Delirium, who is impulsive to the point of, well, delirium. The only character who is more of a blue oni than Dream is the eldest sibling Destiny (and this one without the inner turmoil).
Wolverine (Red Oni) and Cyclops (Blue Oni) - Wolverine's color may be yellow, but he's easily the Red Oni of the team.
Cyclops is probably the Blue Oni for everyone in the team too, and honestly most people he interacts with in the Marvel Universe as well. Ironically with his relationship with his brother Havok, their signature energy colours are reversed.
X-23 also serves as Blue to Wolverine, which stands out even more because she's his teenaged Opposite-Sex Clone.
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.
Superman Reborn reveals Superman is actually both ends of the trope. When the New 52 continuity was created, Superman was separated into his pre-Flashpoint and New 52 selves. The younger and brasher N52 Superman is red while the calmer and more mature pre-Flashpoint Superman is blue; even having the same aura colors. This is clearly a reference to the Red and Blue era. At the end of the story, they combine into a single, complete version of Superman; ensuring his integration into the new DC Universe.
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 Electromagnetic 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 usually unrestrained and selfish Red Oni (red is Rage, orange is Greed, and yellow is Fear) while the "cooler" ones are calmer and often focused on others as Blue Oni (green is Willpower, blue is for Hope, and indigo is for Compassion). The seeming exception is the Star Sapphire Corps, who wield the Love-associated violet; their color is ostensibly one of the "cooler" ones on the upper half of the spectrum but they're easily as passionate as the "warm" Corps (may be a case of Shown Their Work though, as Violet is defined in color theory as a mixture of mostly-red with some blue...meaning warm color range, despite being next to the "cool" colors). The Sapphires generally represent the Red Oni in stories where this dynamic would be present (e.g. when being contrasted with Green Lanterns), but in recent years many of them, such as Carol Ferris, embody the more flexible and positive variation of it. It's been noted that Love is the opposite of the hate-driven Rage of the Red Lanterns, so one could easily see the two Corps as being an exploration of the flip sides of the same Red Oni coin.
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). It's not just unexplained phlebotinum, either; the canonical explanation is that the Blue Light of Hope is breaking the hold of the Red Light of Rage, which by proxy means allowing the Red Oni mentality of the Red Lantern in question to relax a little. Subverted with the Violet Light of Love in that case though; as noted, Love in the Emotional Spectrum is still clearly Red Oni territory, just more positive than the Red Light of Rage...yet it can be used to protect a Red Lantern or former Red Lantern from some of the ill effects of the equally Red Oni-style Red Lantern Power Rings. Played straight outright though in Green Lanterns with Green Lantern Power Rings, based on Willpower, which is ostensibly more "stable" ala a Blue Oni - one of which is used in that spin-off series at least twice to cure someone of the Red Light of Rage
The spin-off series Green Lanterns centers on a pair of Green Lanterns who exactly fit this trope, to the extent it's basically a buddy cop story with superheroes: Jessica Cruz is a genial, cautious, anxious person prone to planning ahead, focusing on strategy, and feeling that they should work as part of a team or remember to ask for backup (Blue Oni), while Simon Baz is a brash, outspoken, impulsive guy prone to jumping in head first without a plan and without waiting for backup (Red Oni). Bonus points for them also fitting the Action Duo trope (with Jessica as Action Survivor and Simon as the Action Hero half), as that trope often overlaps with this one.
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.
As for heroes, the Autobot Clones fit the trope. Although both are Red in color, Fastlane is boisterous, energetic, and rude, While Cloudraker is intellectual and more mature.
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 eyes 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 Parker (Blue) and her clone April (Red) have elements of this, especially once April turns into Dark Action GirlBlood KnightMayhem. Their color schemes are the opposite of their personalities, though.
May can also be seen as the Red to Darkdevil's Blue thanks to their Cousin Yin Yang.
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.
In Tintin, Tintin is calm and smart (blue) in contrast to his hot-tempered friend Captain Haddock (red).
In Astérix, Asterix is cunning and relatively laid-back (blue) in contrast to his emotional and sensitive best friend Obelix (red).
Joe Quesada has made statements expressing this sentiment about DC and Marvel in general, likening the former to a very proper Asian family and the latter to a loud, boisterous Italian family. Bonus points? DC's logo is blue and Marvel's is red.
In Magekiller, Marius is very quiet and reserved. His partner Tessa is somewhat impulsive and never shuts up.