Wade Duck in the U.S. Acres segment of Garfield and Friends fits this trope to a T. In fact, most people's favorite character of the series is Wade, even those who did not like U.S. Acres so much as Garfield.
The fans loving Wade so much was spoofed in the episode "The Midnight Ride of Paul Revere's Duck". Roy only gets one fan letter for himself. After he cries, he sees Bo drive a truck with hundreds of fan letters for Wade.
In the old Beany and Cecil cartoons, resident grownup Cap'n Huffenpuff retreats to his 'secret hiding place' at the first sign of danger.
Although, as he says in "Ducking the Devil", he's "a greedy little coward", meaning that greed takes priority to fear. At the end of the cartoon, Daffy actually beat up the Tasmanian Devil to get back one dollar that the beast had snatched.
That said, many of his actions are more in accordance with those of a Dirty Coward, ready to sacrifice others to save his own skin, without bothering to find out about whether its even necessary and bragging and attempting to victimise others until he bites more than he can chew -which is most of the time. He is such a failure though that he ends up being lovable anyway.
Hurra from Hip-Hip and Hurra. His partner, Hip-Hip, can easily fit this trope as well.
Ringo lampshades this in The Beatles cartoon "Penny Lane" as Paul insists on making haste to Liverpool to thwart what he thinks is a plan to rob the Penny Lane district:
Ringo: Not so fast! Paul: Don't you want to be a daring hero? Ringo: Who wants to be a hero? I'd rather be what I am...a handsome coward!
Tom DuBois from The Boondocks. He's a Nice Guy, but very quick to cry and panic. It doesn't help that he has an extreme phobia of getting raped, which means he tries hard to stay out of prison by not committing any crimes.
Frizz and Nug of The Dreamstone, Frizz slightly more so. They're Dirty Cowards storywise (they are supposed to be villains), but one can't help but love them.