Crime Zone: Shiro often finds himself tearing up and running away in battle. But that is because he's an ordinary human surrounded by vampires and vampire-human hybrids, all of whom are capable of tearing grown men apart limb from limb. When it comes down to his safety or theirs however, he'll gladly give himself up to the vampires out to kidnap him if it means his friends are spared.
Big Windup: Mihashi. Although you're supposed to take his backstory of bullying seriously, his nervous tics are mostly played for laughs. He mostly expresses this by being an Extreme Doormat to his catcher Abe.
Protagonist Dr. Onotera in Emerging, at least in the beginning. He freaks out twice during his initial operating room examinations of victims of the virus... a mistake that could have cost both his life and the lives of the other hospital staff. Despite this, it's easy to root for him as he attempts to overcome his fears and put a stop to the disease spreading through Tokyo.
A somewhat non-traditional example played for absolutely no laughs is Toru Mutou from Shiki. Toru is at heart a good person, and starts off the series being a squeaky-clean Nice Guy popular with the jerks and the cool kids in Sotoba— but once he becomes a vampire, he has to start killing people in order to survive. Which he does, time and time again. He mourns the deaths of those he kills, but he never even considers stopping because he's terrified of dying himself, and of being punished by the older vampires who threaten his family. What stops him from being a Dirty Coward is that he never really loses his good-natured personality, and when another vampire begs him to let her still-living friend go, he eventually complies.
In the early stages of Kenichi: The Mightiest Disciple the main hero Kenichi would sometimes hide or run away from the thugs hunting him both due to his fear and his knowledge that he was incapable of defeating them. As the series goes on this becomes less and less of the case, and every time Kenichi runs its less out of cowardice and more about living to fight another day. "Strategic Retreat" indeed.