I think it might be best if the Joker himself was considered the new Batman. While in prison, the Joker has become a symbol for the down-trodden people of Gotham. With Batman considered a dangerous criminal, the people that used to look up to him as their defender have turned to the Joker, seeing him as a martyr in the fight against the corrupt Gotham officials. However, instead of having another actor play the role, just have him killed off-screen before the movie begins in prison. When he dies, hundreds of the people that believed the Joker a hero don his distinctive face paint and take to the streets, calling themselves "Jokers" (a nod to the gang in Batman Beyond). The lead Joker could be Harley Quinn. In fact, the movie could open with a riot started by the Jokers, and the scene ends with Harley and all the Jokers put back in Gotham.
This is where Bane enters the scene. In this movie, Bane could be the new head of the League of Shadows...or what's left of it, that is. This time, their plan in Gotham isn't to let the city destroy itself, but to save it from its oppressor - the Bat. Bane, like his comic book counterpart, could start a prison breakout to try and lure out Batman. During this breakout, Harley Quinn could escape.
After she escapes, she's quickly contacted by someone claiming to be the second Joker and asks to meet with her. Intrigued, she follows through and is greeted by a man dressed completely like the Joker (save the make-up) but in a green suit instead of a purple one. After hearing his plans, Harley is more or less unimpressed. She would say something along the lines of "You sound like him, but your jokes aren't as funny. They don't even make sense. They're more like riddles. You're not the Joker, you're the Riddler!" I think that would be a good way to include the character's otherwise cheesy moniker.
Throughout the film, the Riddler could be manipulating characters from behind the scenes, and is only actually seen maybe three times throughout. Besides manipulating Harley, he could also be an unknown informant to the head of the division of the Gotham Police put in charge to capture Batman, Harvey Bullock. In other words, the relationship between Bullock and the Riddler would be analogous to the relationship between Gordon and Batman.
Bullock could be portrayed as a foil to Commissioner Gordon. Unlike Gordon, Bullock fervently believes that Batman is a menace to the city. Furthermore, he holds a grudge against Batman, seeing him as the reason that not only have the criminals gotten worse, but also making the police seem obsolete. His desire to see the Batman taken down drives him to accepting the Riddler's help.
In the film, the Riddler's motivation would be to solve the toughest riddle in Gotham City, the riddle that the Joker couldn't even solve. "How do you bring down the Batman?" He figures he can do this by solving another riddle: "Who is the Batman?"
Something that must be incorporated into the film is Rachel's funeral. At this funeral, Bruce could run into one of his childhood friends, Thomas Elliot, who reveals that he, too, was in love with Rachel, even while he was in prison. The Hush persona would not appear, only the Elliot character. Elliot, like his comic counterpart would be recently released from prison, and as part of his parole must see an anger therapist three times a week. His therapist would be Hugo Strange. Strange could be a closeted Joker fanatic and also in contact with the Riddler. Under the Riddler's orders, Strange could slowly and surely make Elliot's anger grow and have it directed at the Batman, whom Strange would make to seem was responsible for Rachel's death. The Riddler plans on using Elliot as a weapon that could be used to kill the Batman once he has been unmasked.
In a bit of a minor change, Kirk Langstrom could be Fox's replacement at Wayne Enterprises. The Man-Bat character wouldn't appear as it would be too unrealistic for Nolan's universe.
The film would come to a climax with the Riddler telling Harley to do lure Batman into a fight under the pretenses that it's a trap. It is, but the fight with Harley is only to get Bane's attention. After beating Harley and her Jokers, Bane attacks a weary Batman. Although Batman eventually wins the fight, he's been greatly fatigued. The Riddler leaves a clue to Bullock to go where the fight with Harley and Bane are, and, unable to escape, Batman is arrested.
Seeing on the news that Batman has been captured and unmasked as Bruce Wayne, Elliot would go to the courthouse and attempt to kill the man he sees as responsible for Rachel's death. The point of the scene would be to mimic the scene from Batman Begins where Bruce goes to the courthouse to kill the man who killed his parents. Elliot's attempt ultimately fails.
And after that, I don't know what would happen. Sorry this is so long
