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.
Bret Maverick. The entire Maverick clan, of which there are a massive number, have made cowardice their family motto for generations.
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?
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.
Kaamelott's Bohort. He's 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.
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.
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.
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 competant would likely take over.