Professor Gilderoy Lockhart in Harry Potter and the Chamber of Secrets, to an extent. It's not explicitly confirmed that he's an inherent coward, but he's admitted he didn't do the things he has claimed to have done. On an interesting twist, he is actually a somewhat accomplished wizard... being an expert in memory charms to make the people who ACTUALLY did the things he claimed forget they ever did it.
Interestingly, Lockhart was one of the very few characters based off real people. The real person, according to J. K. Rowling, was "even more objectionable than his fictional counterpart" and is probably going around claiming that he was the inspiration for Albus Dumbledore.
Fflewddur Fflam, from Lloyd Alexander's Chronicles of Prydain. Slightly mocked in that he suffers a consequence every time he lies or tells an exaggeration (namely, a string on his lyre breaks). This consequence is used to highlight the fact that he Took a Level in Badass at the end of the first book, when he claims to have fought in the last battle with unbelievable bravery and skill, and turns out to be telling the exact truth. He's a very sympathetic take on the trope; in the subsequent books it becomes clear he really is brave and a hero, he just can't resist exaggerating.
A prequel short story makes it clear that he was always a badass, almost to the point of foolhardiness; at one point, he defended a lone man attacked by a group of bandits without hesitating and lept into a raging current to save a stranger from drowning. In fact, most of his early lies in the prequel story are simple modesty ("No, no... it was no trouble at all, and I needed a bath anyways...")
One Forgotten Realms anthology had a short story of the member of an explorers club and how he was hailed by everyone as a hero and an example to look up to. The 'Hero' makes a living getting free drinks and meals telling of his adventures. Eventually Cyric, god of lies, captures him and points out all his lies such as he was the sole surviver of a battle because he ran away. The 'Hero' is dragged down to Hell to the sounds of everyone abusing him. Although you'd think the God of Lies would commend him for this, he's also the god of murder and insanity. Don't look for too much logic in his actions.
Professor Nimrod Pennyroyal from Mortal Engines claims to be an explorer / gentleman adventurer in a series of best-selling books, but turns out to be a liar and a coward.
Inspector Friedland Chymes in Jasper Fforde's The Big Over Easy is the best detective ever! He's a genius who always gets his man, who singlehandedly put away an Axe CrazySerial Killer, and whose exploits are the most read in all the magazines and papers. Except, of course, that he makes all his cases up, he stole the credit for his greatest success from his partner (who was the man who actually caught the Axe CrazySerial Killer) and who runs away from the first hint of danger in a cowardly panic.
Ciaphas Cain takes this trope all over the place. Cain is hailed as one of the great HEROES OF THE IMPERIUM!!! His demeanour in person is the very humble and modest "it was a team effort" of any true badass. Cain himself thinks he's a rank coward, who is more than willing to milk his reputation and play the "bluff old campaigner" to reinforce that reputation. However, a bit of reading between the lines shows that while Cain tries to avoid danger whenever possible, he is highly skilled and effective in his duties as a commissar, and when pushed into danger, he will pretty much always come up smelling like roses.
The hero of most of the Vorkosigan Saga, Miles. A rare sympathetic example; he wants desperately to have the status that comes from Military Service on his homeworld of Barrayar, to prove that he is not just his father's son but someone in his own right. He has to avoid direct combat whenever possible, however, as he's under five feet tall and (at least initially) has bones like glass. His solution? Copious quantities of smarts and an utter refusal to ever, under any circumstances, give in.
Later in the series, Miles becomes a complete inversion of this trope: He has been responsible for saving the Empire on several occassions, his cover identity has been awarded medals by several different planets, and he is regarded as such an important asset that he is a strong contender to be the next Chief of Imperial Security... but since every single act of heroism he's performed is highly classified, he can't tell anyone about it.
Surprisingly, Sir Lancelot is one of these in Bernard Cornwell's Warlord Chronicles. He employs the spinmeisters of the day (bards) to tell his "Great deeds", plunders the battlefield after the fighting has ended for his "Spoils of victory" and is not above giving himself cosmetic cuts to show how hard he had fought. This policy is so successful that, even though the narrator actually knew Lancelot and was responsible for his execution for treason, he is told by one of those to whom he's recounting the tale that his tale is clearly wrong, as it doesn't match his "legend".
This is something the narrator is quite irritated about. Lancelot is so bad, that the narrator struggles to come up with anything good about him. This is possibly the only moment when Derfel (the narrator) is actually bitter.
Paris from The Iliad, making this trope Older Than Feudalism. He jumps in front of the Trojan lines (wearing a leopard skin no less) and challenges the best of the Greeks to face him. Menelaus is happy for a chance to punish him for stealing his wife, but as soon as Paris sees Menelaus he falls back behind the Trojan lines, much to the chagrin of his more valiant brother Hector.
Ares, of all people, shows a touch of this in The Iliad. He's helping his humans of choice, the Trojans, by running amok on the battlefield with Hector. Athena and Hera, patrons of the Greeks, decide they've had enough, with Athena asking Zeus' permission to interfere. He grants it, and Athena goes down to the battlefield, gives Diomedes divine assistance, allowing him to wound Ares in the gut. Ares lets out a scream that stuns the entire battlefield... and then flees back to Olympus, complaining to Zeus about how his bitchy daughter and an uppity mortal dared to hurt him. Zeus basically replies, "Oh shut up. You're just like your mother."
Warden Ramirez is the regarding his success with the ladies in The Dresden Files. He's actually a virgin. The timing of the reveal is unfortunate from his point of view. When this is revealed (by a succubus no less), Harry spends the rest of the time ribbing him. In actual combat, he is more than competent. It takes skill to make regional commander in the Wardens on a war footing before you're 25.
The Eebs from Changes seem to be a villainous example, as they're evidently hailed as the best assassins in the Red Court, yet spend most of their run-ins with Dresden fleeing for their lives or shoving their own mooks in his path to die in their stead.
"Not gor-illas dear lady, por-illas. A species of South American wombat, and very good eating they make, too"
Iorwerth from The Valkyrie's Tale. He presents himself as a knight whose stories about the battles he's fought are brilliant and entertaining. Of course, this is because he's a bard pretending to be a knight; making up stories is what he's best at.
Jan Onufry Zagłoba from Sienkiewicz Trilogy. He boasts about his accomplishments (others had achieved with little to no help from him) and is prone to overplay his courage and battle prowess. To be fair to him, however, he's incredibly cunning, which has saved the heroes from serious trouble more than a few times, and isn't really that much of a coward (he just doesn't like to put himself in unnecessary danger).
The Imperial Commander Fuzzel in Galaxy of Fear: The Brain Spiders is believed to be this. He's very gung ho about tracking down criminals and talking about how they'll regret meeting him and the pain he'll deal out, but no one really believes it's more than talk. His weight is a factor in this. When he actually does face one of the criminals... said criminal is unrecognizable thanks to a Grand Theft Me, and Fuzzel's caught by surprise and killed before he could display courage or a lack of it.
British statesman Lord Chesterfield in Letters to His Son: "I say suspect them, for they are commonly impostors; but do not be sure that they are always so; for I have sometimes known [...] blusterers really brave"
The man himself shows up at The Captain's Table in the Star Trek: New Frontier novel The Captain's Table #5: Once Burned. He's a Roman legionnaire who blusters about how a 16-year-old boy (one M'k'n'zy of Calhoun) has taken his table. He relents after said boy gains the upper hand and pins his beard to the table with his own knife.