In the 1990 first season episode of Tiny Toon Adventures, the episode Cinemaniacs! had Babs and Buster Bunny theater hopping (rabbit style) with each flick getting a segment of the episode. The first short titled Superbabs put Babs Bunny into the iconic blue and red. I suppose this may actually be a Supergirl parody, but the villain, Wex Wuthor is of course the parody nemesis of Superman. Essentially, Superbabs stopped Wex from inking Acme woods.
This was reasonably cute, but I don't consider it near the classic of Super-Rabbit or Stupor Duck. Though I appreciate the extra effort to also give Batman a quick shout out.