"I was once placed between two waxworks on a programme where one of the pair was solemnly identified as a 'liberal'; appropriately, he seemed to have been dead for some time, while the conservative had all the vivacity of someone on speed... On air, I identified the conservative as a liberal and vice versa. The conservative fell into the trap. 'No, no!' he hyperventilated. 'I'm the conservative!' It was the liberal who got the point; from beyond, as it were, the grave he moaned, 'He's putting us on.'" —Gore Vidal
Icon from Milestone Comics was created by a black liberal writer as a supposed black conservative. However, the in-story reason for him being a conservative is that he was born in the days of slavery when the Republicans were on the anti-slavery side and in modern times his sidekick started convincing him that conservatism is bad for the poor. This doesn't exactly fit the definition, but it approaches it. It's as if the writer wanted to put a conservative in, but as the trope description says, couldn't think of any way for a reasonable person to be one today. This is a complicated example, as "liberals" and "conservatives" of 150 years ago share very few traits with their counterparts of today except for the names, not to mention that he's a two-century-old alien ex-slave and probably wouldn't think like a modern human anyway.
The DCU: Decisions election issues were designed around superheroes expressing political opinions about the 2008 election. The problem was that all of the Presidential candidates were fictional and there was no real sense of anything they stood for. Green Arrow seemed to be voting for the Green Party and Lois Lane seemed to be Republican (or possibly a Libertarian?) but everyone else's opinion was just obtuse. In the end it seemed to come to a conservative-leaning writer (Bill Willingham) and a liberal-leaning writer (Judd Winick) picking heroes like they were choosing players for their kickball team. Needless to say, the whole story caused a Flame War. Green Arrow's (left wing) and Hawkman's (right wing) political views were already well-established for years, but the idea of ascribing definite political views to all the other characters resulted in fans hysterically fighting over which characters "should" or "shouldn't" belong to which party.
Julia Shumway, the Informed Attribute Republican editor of the newspaper in Stephen King's Under the Dome, is considered by some to be the conservative version of a Fox News Liberal. On the one hand, she doesn't talk about politics at all, and the only reason to believe that she is a Republican is because the author says she is. On the other hand, almost no one (who is sane) mentions politics at all because, well, they're trapped under a dome, and sometimes little things like that have to take precedence.
Live Action TV
The West Wing, like most Aaron Sorkin shows, makes heavy use of Strawman tropes, including this one, despite attempts to resist using them.
Ainsley Hayes, the Trope Namer for Blonde Republican Sex Kitten (with a touch of Southern Belle). Presented, at first, as a strong Republican that had previously been a member of the Federalist Society and could smack around expert liberal debaters, she quickly lost or strongly downplayed her initial displeasure about pork-barrel politics, gun control, and what she saw as unnecessary legislation. Her quick decision to leave gun control off the discussion table in response to a politician's attempted assassination is a particular moment, coming as it does from a Ronald Reagan Republican.
Arnold Vinick, the Republican presidential nominee in the final season, rejects enough Republican principles that it's almost impossible the real-life Republican party would nominate him for president. He's pro-choice and not at all religious, although he's a big believer in economic conservatism, as in big tax cuts and reducing the size of government. Vinick's strong economic conservatism would not go far in the Democratic party, and he's not extreme enough to be accepted by the Libertarian party, so he's more of a Republican than anything else. Of course, he's from California, where Arnold Schwarzenegger, with similar views, was successful as a Republican politician, so his being a Republican Senator is believable. But as for his presidential nomination....
Actually Vinick is very similar to real-life "establishment" Republicans, a few of whom had indeed been the Republican nominee for president. Where Vinick starts to be unrealistic is that he doesn't apologize for, or walk back, any of his more liberal positions in an effort to convince the Republican base to vote for him. He would have to in order to be so much as nominated.
In fact, pretty much any Republican character whom the audience is supposed to like and respect gradually becomes one of these if they're around long enough. One particular exception is Speaker of the House and Acting President Glenallen Walken, who proves to be a competent president and reasonably likable man of integrity despite also being clearly depicted as a conservative Republican and military hawk. However, he was only around for three episodes, it's possible this wasn't intentional and in any case, he was played by John Goodman, which goes a long way.
Meanwhile, everyone who appears on the show and is to the left of the main characters seems to adopt the characteristics that Fox News associates with liberals: they are, almost to a person, shrill, mean-spirited, short-sighted, and egocentric. This is especially notable in any episode dealing with free trade, where opponents of free trade always get portrayed as hypocrites, grandstanders, or idiots. Basically, the door swings both ways: if Aaron Sorkin disagrees with you, you're either a nut or a meanie, and it doesn't matter what side of the political spectrum you fall on.
In the case of free trade, the protagonists all worked for President Bartlett, who was a Nobel Prize winning economist. Still true now, although even more universal at the time The West Wing aired, virtually every economist, left or right, supports free trade (for example Paul Krugman in real life is a Nobel Prize winning economist to the left of Bartlett who was very strongly for free trade) so it would have been inauthentic to do anything other than portray him and his staff as disdainful of protectionists.
The French Police showP.J has Chloé Matthieu, who is a Fox News fascist — she starts as a member of a far right Police Syndicate, her uncle ran an election for a far-right party (not named, but probably this real life party), she seems to hate anything and anyone having a common point with Arabs, Muslims, human beings with dark skin, homosexuals... Yet she manages to become good friend with Muslims and/or black policemen, has a child with a black man, works part time in a lesbian bar, asked a bisexual colleague to help her take care of her child when she has to work late, and implicitly admits than most of her opinions are bogus. This is a case of the trope being used as character development: she starts as a straw man, and then progressively realizes how evil her beliefs are during the course of the show.
Entertainment Weekly editor Mark Harris wrote an article about this, specifically naming Harriet Hayes of Studio 60 and Kitty Walker of Brothers and Sisters.
The main character is Will McAvoy, a conservative news anchor who repeatedly criticizes the current state of the Republican Party. In the first few episodes of the show he mocks Sarah Palin and rails against the Tea Party.
In-universe, News Night can't get a good conservative representative to support SB 1070, so they're forced to get a bunch of idiots and wack jobs who don't know the issues. McAvoy has to make their own arguments for them and feels that the show dropped the ball.
In-universe, one episode of All in the Family has Archie Bunker complain to a local TV station about a pro-gun-control editorial. After he confronts the station manager, he's offered airtime to present an opposing view, with the clear implication that the manager is cynically satisfying the letter of the then-extant Fairness Doctrine while making the pro-gun side of the argument look bad.
Parodied in The Simpsons episode "Politically Inept with Homer Simpson", where a network executive tells Homer that they only have a few political pundits on staff, including their liberal strawman. Cut to an over the top left-wing stereotype singing "Oh, the plain and simple fact is, I'd love to raise your taxes, and make your children gay..."