Merton J. Dingle from Big Wolf on Campus. Despite being a guy who has hidden behind girls during fights with supernatural beings, has regularly redirected the Big Bad towards his best friend and show's hero in order to keep himself safe and has outright apologised to enemies if a plan or strategy he used against them doesn't work; he's still an incredibly lovable (and funny) character.
Captain Blackadder in Blackadder Goes Forth tries everything to get out of the war, but since the war is portrayed as a completely pointless waste of human life, the audience roots for him. In fairness, he shows considerable bravery in the face of danger; it's just that he doesn't want to face danger in the first place.
Vila from Blake's 7: cowardly but cute and funny, and able to unlock any door to get himself or other main characters out of trouble...
Vila: There isn't a lock I can't open... if I'm scared enough. Blake: Are you scared enough for that one? Vila: What d'you think?
The Bugaloos: Sparky is a firefly who is a coward and is lovable. His courage is put to the test in some episodes.
From the original series is Vislor Turlough, who has the uncanny ability to save his own hide in every dangerous situation. He's pressured by the Black Guardian into attempting to kill the Doctor, was accused of (planning to) kill someone (to which everyone protested since that's against his nature), and, in the Big Finish Doctor Who audio dramas, even convinced a Sontaran that running and hiding from scary monsters was the best thing to do for the entirety of a story. He's still somewhat well-liked by the rest of the team, though.
Game of Thrones: Samwell Tarly is scared of absolutely everything. Subverted completely in "The Watchers on the Wall", in which he voluntarily joins in the defense and keeps a cool head before and during the battle.
Sgt. Schultz in Hogan's Heroes really just wants to keep things nice and quiet and peaceful on his shift and definitely doesn't want to get involved in anything that might look like trouble — and given who he has to work for, you really can't blame him either. He's petrified of the idea of being sent to the front lines (and Hogan and his men do their best to prevent that from happening to him and Colonel Klink, seeing as if it did happen, someone competent would likely take over.
Kaamelott: Bohort is mostly a coward, but then again, his all-around good nature makes him rather endearing, all the more so since many other characters are brutes. He also doubles as a Crouching Moron, Hidden Badass on occasion.
In The Magnificent Seven (1998), Ezra freely admits that he's a coward, but always comes back to save his teammates and do the right thing.
Maverick: The entire Maverick clan, of which there are a massive number, have made cowardice their family motto for generations.
Patrick Jane of The Mentalist sometimes acts as this. His cowardly moments make him more endearing because it reveals that under his cool facade he still experiences the same fears as everyone else.
Rumpelstiltskin in Once Upon a Time before he became the Dark One. He ran from War and was forever branded a coward. He became the Village Coward, everyone hated him, and his wife left him for a pirate. The sad part is that he ran so his son wouldn't grow up fatherless like he did. He ends up losing his son anyways.
Rimmer of Red Dwarf is a Dirty Coward, a consummate backstabber, a human danger detector... and also, as he points out himself, rather sweet. Sometimes. He improves over the course of the series.
Rimmer: Follow the Rimmer-shaped blur.
Supernatural: In "Bad Seed", Claudette is a pleasant and humorous character who immediately runs away when an assassin shows up and helps the Winchesters capture Rowena so Crowley will call off the assassin who almost killed Claudette.
