Do you have to pay royalties for performing a Batman/Joker stunt show at a convention?

You would need to get permission from the rights holder and that permission may include a requirement to pay royalties. Lines from the comics would raise copyright concerns, but the first hurdle is overcoming the trademarks issues.  I think Time Warner owns DC comics and has licensed its rights to live entertainment, at least in part, to the Six Flags owners. You'd be better off having a stunt show featuring a dark, brooding anti-hero character battling a crazy psychopath. If you can keep to the comic book stereotypes and not do anything to identify with those specific characters, you could avoid licensing while using a generic storyline with which your market is comfortable. Good luck, Todd