Trying to stick to the good-guy, bad-guy formula here...
- Bugs Bunny as Superman.  Plain and simple. 
- Daffy Duck as Batman.  Batman more than anyone else is Superman's opposite in the JLA, the flipside of his coin.  Bugs and Daffy occupy the same slots.  Plus, Daffy's had a few Batduck cartoons under his belt anyway. 
- Road Runner as Flash is good.  Or Speedy Gonzales if you wanted to be non-PC.
- Porky has to be Robin, seeing as how his best work was done as Daffy's sidekick.
- Wonder Woman?  As much as I hate "Space Jam", I guess Lola Bunny's your best bet.  She's the only memorable female Looney Toon ever.
- Hawkman - Foghorn Leghorn.  Why the hell not?  
- Tweety Bird takes the position of the Martian Manhunter.  Look at the shapes of their heads.  Both freakishly big.  Both fairly round.  That's the key.
- Green Lantern could be... uh... somebody... the first unused good guy Looney Tune I can recall.  Maybe Pepe LePeu.  Sure, whatever.  I'm grasping at straws now.
The Bad Guys - 
- Elmer fudd as Lex Luthor is the only logical choice.  
- Sylvester - well, based on name only, I guess that makes Sylvester Sinestro.  Sylvestro.  I like it.  
- Marvin as Braniac, still perfect. 
- Taz... Joker?  Nah.