Well some in the gay community consider the X-Men films to be about gay superheroes. There are many parallels between homosexuals and the mutants of the Marvel universe. There are even little nods and winks in X2 towards that perception (Bobby's "coming out" to his parents, and his mom's response of "Have you ever tried not being a mutant?"). I remember reading an article that the gay community was upset that X3 wasn't "as gay" as X-Men & X2. The only X-Man that I know of who's openly gay is Colossus (so in a way, X2 & X3 are gay superhero movies).
As for a new superhero movie, with a hero created specifically for the film and not based on any existing comic book characters? That's kinda tough. Like others have said, if you make a movie about a gay superhero just for the novelty of making the superhero gay, it probably would not work. I certainly wouldn't bother to see it. But if you were to make a good superhero movie about a superhero who just happens to be gay, then I might go see it.
Incidentally, I happened to stumble across a satirical superhero comic a number of years ago in a thrift store. It was called The Gay Avenger. It was about this family of Batman style vigilantes. It was a tradition passed down through the generations that the man of the house would take on the mantle of The Gay Avenger. The tradition started way back in the 1920's during the time of mobsters like Al Capone. When the first Gay Avenger started fighting crime, the accepted definition of the word "gay" was "happy" (as in "Don we now our gay aparel"). But in the 1960's, the Gay Avenger's son was sent off to fight in Vietnam, where he lost a leg. Thus he was forced to skip his turn as The Gay Avenger, and as a result people began to forget about this masked vigilante. But the last official Gay Avenger's grandson is now of age, and is going off to college. He grew up on a farm though, in a fairly conservative rural community (and I'm not sure, but I think he was also home schooled), thus he was fairly naïve. Then while at college, he dons the mask and tights and goes out to fight crime as The Gay Avenger. The first crime he thwarts is a gang of neo-nazis calling themselves The Intolerants who had busted into a fundraiser and had taken the guests hostage. The press is there and they take his picture as he proudly announces himself as the hero The Gay Avenger. However, he's completely oblivious of the fact that the fund raiser he had rescued was for the LGBT community, which leads to a whole confusion about his sexual orientation (the character's straight, and he still considers the definition of the word "Gay" to be "Happy").
I know that's not exactly the story you had in mind, but this whole subject matter just kind of reminded me of that comic book. Unfortunately I didn't buy it at the time (I didn't even have the $0.50 it would've cost me at that time), and I have no idea of who wrote or published it. I tried googling it once. All I found was slash fiction of Marvel's Avengers, with Thor getting it on with Iron Man, and Black Widow getting it on with She-Hulk. Anyway, I just thought I'd throw in my 2 cents worth.