In Misfile, Rumisiel's presence is explained as being Ash's Canadian exchange student live-in boyfriend. Since the story takes place in Massachusetts, this is regarded as being a little implausible to say the least.
City Under The Hill has this Trope often invoked by Slim on topics ranging from whether or not he stole evidence from a crime scene, to whether or not he's ever going to pretend to obey the law.
The Guacans of the Punyverse arc will insist that they do not eat people, even while sharpening cleavers and warming up the cooking pots. "Come to Chau-5, we won't eat you!"
In "Aylee", after a 50-foot-tall Aylee runs through the suburbs causing mass destruction, she retreats into her shell and tries to pass herself off as a volcano. When the mob chasing her wonder how a volcano wound up in New Jersey, Aylee tells them global warming did it. Everyone finds this perfectly plausible and never question the fact that a volcano just answered their question.
Red Mage and Thief use this when Ranger asks why they betrayed his group:
Thief: Ghosts. Red Mage: Aliens. Thief: Ghost aliens. Red Mage: Who possessed us. Thief: From space!
Warmech is especially prone to this.
Black Mage: Oh, Lord, why does the robot have a mustache? Warmech: I grew it with my human lip. [later] Warmech: BEHOLD MY HUMAN LASER! [later] Warmech: I HAVE NO LASERS AND WILL LASER TO DEATH ANYONE WHO SAYS OTHERWISE.
Gabe: You said this would be easy, a half an hour tops! My world is pain! Tycho: Gabe, sometimes in order to hurt someone very badly, you have to tell that person terrible lies.
Buck Godot engages in a bit of this toward the end of the Psmith storyline (warning: spoilers!) towardtheend, when he alternates between telling Psmith one thing and Der Rock the precise opposite, in front of them both.
In Questionable Content, comic #499, Jeph writes in his little blurb at the bottom of the page "Comic number 500 is Monday. I don't have anything particularly special planned, but who knows." for the entire run of QC previous to this, Faye and Marten's possible relationship had driven most of the plot. In comic number 500, the two of them resolve the situation and the plot progresses. Faye likes Marten just fine, but she has lingering trust issues and can't maintain a relationship. Everything works out just fine, and they're still roommates.
Also present in several scenes where Faye knocks someone out, then explains their unconsciousness with "Owls." when they wake up.
In The Order of the Stick, Haley has a Bluff Skill that is ridiculously high, letting her get away with almost anything.
Turned Up to Eleven in this strip thanks to a potion of glibness. This is consistent with D&D 3.5 rules - If your Bluff check beats your opponent's Sense Motive by 20 or more, you can get them to believe things that are actually impossible. Glibness adds 30 to your Bluff check.
Dillon's agent in Ménage à 3, attempting to explain away the fact that he's in a Transparent Closet. And the best part? Not only does the agent seem to believe it himself, but Dillon thinks it's credible because Oprah presumably said it.
Dillon: You know...it's none of my business...but someday you will have to tell your wife you're gay. Dillon's Agent: Ho-ho-ho! Don't be silly! I'm not gay! That's why I have you wear the wig! Dillon: I think it might be a little bit gay. Dillon's Agent: Dilly...straight married men have secret gay sex all the time! Dillon: That sounds made up. Dillon's Agent: It's true! It's called "being on the down low". Saw it on Oprah.
From the same universe, this was how Lavali of Sandra on the Rocks tried to stay in her extremely Transparent Closet every time her parents and/or brother would catch her in a compromising position with a girl. Which was often. None of them bought her flimsy excuses for a second, but she somehow got the impression that she had masterfully deceived them all.
Each update of "No Black Plume" comes with the authors' real credentials.
Sandra of Zebra Girl initially trying to cover up her demonic appearance starts out very badly at this. Her story about the origins of her "scars" involves low flying birds, a ladder and a room full of knives.
Petey: Captain, you have heard the charges. How do you plead? Before you answer, you should know that if you plead "guilty" you'll be immediately extradited and U.N.S. law will take over. Captain Tagon: Not guilty. Petey:Also, it's not very nice to lie in court. Captain Tagon: But it beats extradition.
In Luminary Children, Lyzza's ability is to make people believe whatever she says, which of course leads to the most absurd lies.
In The Adventures of Dr. McNinja, Victor the obvious spy claims to be plumber — even when he's caught installing a camera on the ceiling, he claims it's a strange toilet. In a later story, when he's caught having been hiding in the Doctor's office for ages and taking part in specific political intrigue that he's confessed to, he still presents a plumbing bill.
In Operation Reboot, Shae feeds a story to her mother that is completely absurd (though much less so than her brother's). Hilariously, her mother buys it anyway.