Mr. Carlton in WKRP in Cincinnati. He's a nervous and henpecked man, but he's strongly implied to have seen heavy combat in World War II bloodbaths.
Has his finest hour when he stays on the air during a tornado. "Sometimes we have to be very brave even when we're not."
Vila Restal of Blake's 7. There isn't a lock he can't pick, especially if he's scared, and when backed into a corner he can show surprising courage. This is the man who bluffed Servalan and an eight-ship battle fleet into retreating.
Mr. Monk in Monk. He went into a panic about having laser pointers pointed at him by children early one episode. Later he has them pointed at him attached to guns, held by professionals, while keeping a jet airplane piloted by a man he knows is a killer on the ground by standing in front of it. He does the latter while barely flinching.
Star Trek: Deep Space Nine Quark (who had always been portrayed as pretty much a fast talking coward) had a Crowning Moment of Awesome when he stood in front of a Klingon who was nearly twice his height in the middle of the Klingon parliament, after the Klingon had challenged him to a duel to the death, and just looked him straight in the eyes and flat out told him that he wasn't going to fight and if the Klingon wanted Quark dead just to get on with it. This would, of course, deny the Klingon the honor of defeating a foe gloriously in battle (Quark even KNELT), making his "victory" shallow and meaningless. The Klingon went in for the kill anyway, but the Klingon Chancellor stepped in, and declared that if the bad guy would really kill an unarmed opponent, then he truly had no honor and he was promptly discommendated and kicked out of the building. Gowron even compliments Quark on the bravery doing that would have to take.
All told, he shoots down about a dozen super-soldiers over the course of the show when things get serious. A slight subversion, as in his culture talking your way out of things gets you a lot more respect than what other cultures consider heroism.
Neelix in Voyager puts on a show of cowardice (to the point of great annoyance for those around him), but he's a ruthless bastard when he needs to be, like when he dealt with the Kazon in the pilot.
In Teen Wolf, Stiles is one of the only characters with no superhuman abilities or weapons training, but he doesn't shy away from attempting to save his friends and family, scared he may be. And if he has to throw acid at the evil Alpha to buy the other wolves some time, he'll do it.
Connor in Primeval thinks of himself as a cowardly geeky, bookworm, but when it comes to it is just as capable of facing down velociraptors and other nightmare-riffic creatures as any of the more traditionally heroic characters.
The Cowardly Lion's counterpart in Tin Man, Raw. Quiet fellow, empathic, healer, and generally not badass in the slightest...until the climax of the series.
Dr. Rodney McKay from Stargate Atlantis is whiny and cowardly. Somewhat justified as he's a scientist put into a military team. In dire situations however, he always shows astounding courage, with some of his best plans coming to him during duress.
Xander Harris from Buffy the Vampire Slayertalked about being a coward, but would go into danger to help his friends despite his fear.
On LeverageHardison often acts this way, especially in comparison to adrenaline junkie Parker or badass Elliot. While he often complains about the situations he goes into, he never actually backs down.
The Lone Gunmen: Byers is a meek, mild-tempered guy - except when you ask him to look the other way on an injustice. Then, he suddenly develops enough balls to call out one of the most frightening members of The Conspiracy right to his face.
Once Upon a Time: Archie (or Jiminy) was such an Extreme Doormat that he gave up his humanity just to get away from his thieving family. However, Regina made the mistake of trying to trying to interfere in his treatment for Henry. Instant backbone and set of Brass Balls showed up, and he threatened her by saying that he could be a deciding factor if Emma wanted to sue Regina for custody of the kid.
The Second Doctor is the only one who often shows open fear of villains and monsters when cornered by them. (When other Doctors occasionally do it, it's always a serious Oh, Crap! moment.) His Catch Phrase is "When I say run, run!". Nevertheless, he's as heroic in his actions as any of the others.
Turlough, during the Fifth Doctor's run, is a mix of this between this and Lovable Coward. He's only with the Doctor because of circumstances, and runs away from things and hates danger, but when it's needed he mans up and does what's right.
Methos on Highlander: The Series preached the gospel of running and hiding, but frequently walked coolly into danger for his friends.
Monroe of Grimm has elements of this. He is nervous, easily flustered, tries to avoid unpleasant confrontations—but when push comes to shove he will rip someone's arm off, throw a rather hefty man all the way across the room, and rip the throat out of a gun-wielding thug.
Captain Edmund Blackadder of Blackadder Goes Forth always actively tries to shirk dangerous duties, and spends most of the series trying to avoid leaving his trench, but whenever he is thrust into a life-threatening situation (captured, court-martialed, sent on recon missions) he is just as calm and collected as he is sitting back in his safe, warm hidey-hole. Most fans consider him less a coward and more unwilling to die needlessly, and, to be honest, getting out of World War I is a pretty sympathetic motivation.
Don Dogoier/ Gokai Green from Kaizoku Sentai Gokaiger. He hides,trips, falls,and hurts himself by punching his own hand doing a pose. He's also shown to be capable of fending off Mooks with a broom, can land a hurricanrana, and has been shown to be strong enough to crack the mooks' necks on at least two occassions.
El Chapulín Colorado runs around this trope as the eponymous superhero is extremely coward (as it's an Affectionate Parody of Tokusatsu movies). Chespirito always said that this was intentional as the real hero wasn't the one without fear but the one that even with fear still did the right thing.