Bugs' official girlfriend before Lola Bunny was Honey Bunny, created by Robert McKimson for the comics in the 50s or 60s (forget which). Basicially, Honey Bunny was used whenever a girl companion was needed for Bugs Bunny merchandise or comics. Before Honey Bunny, Bugs had a girlfriend in the comics named Lulu Belle. Lola Bunny was created in an attempt to update the Looney Tunes gang by adding a cliched "strong woman" character. Bugs had a bunch of different girls in the various cartoons, and Mrs. Bugs Bunny even appeared in "Hold the Lion Please."
Daffy never had an official girlfriend, but he was (unhappily) married in several cartoons (Daffy's "henpecked" cartoons are all overlooked gems). The wives usually didn't have names, except for one called Daphne. There were also other various girlfriend characters, like in "The Scarlett Pumpernickel" and "Muscle Tussle."
So, at least in the cartoons themselves, Bugs and Daffy didn't have official girlfriends, and I hope it stays that way with these new shorts they are making.
Porky Pig is really the only major character who had a consistant girlfriend in the comics and cartoons, she was named Petunia Pig. I guess Miss Prissy could count as Foghorn Leghorn's "girlfriend," but they really aren't much of a couple.
Penelope the cat is sort of a non-character. The cat in the Pepe Le Pew cartoons often times had a different name in every cartoon, and it was always implied that it wasn't the same cat. Penelope is basically all of the cats combined into one for merchandising purposes.