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.
Finral Roulacase from Black Clover is always trying to avoid fights as much as possible. His magic suits his personality well: it's not particularly good for fighting but it's great for running away. He nonetheless musters up the courage to support Asta with his magic against Vetto. By the time he enters the Royal Knights Exam, he's no longer a coward in any way even though he still can't use magic to attack directly.
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.
In Demon Slayer: Kimetsu no Yaiba there’s the resident nervous wreck: Zenitsu Agatsuma, a seemly cowardly guy who can give others a bad impression at first but he quickly turns that around by being one of the most good natured characters in the series, boasting some real hidden talent only overshadowed by his lack of confidence, whereupon Zenitsu has overcame his fears many times to protect those he cares about and slay demons with his companions.
Dragon Goes House-Hunting: Letty the dragon is a coward who initially tries to run and hide whenever he encounters something scary or dangerous. However, he's so sweet and innocent that one can't help be fond of him. It's not unjustified, either. He lacks any special combat skills while all his body parts are highly sought after by Heroes, so he has good reason to be afraid.
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.
Expecting to Fall into Ruin, I Aim to Become a Blacksmith: Protagonist Kururi's father Toral Helan is a feudal lord who just wants to relax and be a gourmand, while being a caring father, but runs off claiming stomach pain at the first sign of trouble. He ultimately just pushes everything onto Kururi and Hyper-Competent Sidekick Lotson, and approves whatever they say. Toral eventually abdicates and becomes a court painter.
Makoto from GTO: The Early Years is pretty cowardly, but his status as a Butt-Monkey means you almost always feel sorry for him. And he does support his friends, just usually while hiding behind them.
Myoga from Inuyasha will run away every time things get tough. Of course, he's a flea that's an inch tall and couldn't even inconvenience a normal human in combat, much less do anything to the giant demons that the group regularly fights.
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.
Haruka in Kotoura-san is ridiculously timid, and can get scared by her closest friends merely acting tough for laughs. In less serious situations, she usually responds by crying and/or running away.
In Let's Start An Inn On The Dungeon Island, the main character Sanada Shirou is very cowardly and avoids battle whenever humanly possible, and lets everyone know it. The one time he does go into a fight willingly, he's using a "borrowed" magic artifact which arms him out the wazoo, rescues Cecily from a swarm of ogres and the Flunky Boss generating them, then sighs in relief when it's all over, letting others take the credit.
Usopp's cowardice is one of his main comedic traits, though he stays lovable by being a Cowardly Lion where it counts.
Nami to a lesser extent. For example, her preparing to abandon her friends to avoid the wrath of Crocodile, one of the Seven Warlords, is played entirely for laughs.
Rebuild World: Hikaru is assigned as The Handler to Akira, being a sheltered and ambitious woman used to being far from harm, unlike most of the cast, and planning to exploit Akira to advance her own career. After thinking it'll be easy, she comes to the sudden Oh, Crap! realization after it's too late, that Akira has no understanding of how a justice system works (having spent all his life outside of one), and that he's quick to resort to killing. Hikaru spends the rest of the story an Only Sane Woman panicking one way or another while trying to avoid getting banished from her home or worse as a consequence of her own initiatives regarding Akira, as they go From Bad to Worse.
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.
