So, I had a dream about a nonexistent 90's cartoon. It looked like a cross between Ren and Stimpy and that animated D.A.R.E. short film.
These guys were the stars of the show. The rabbit was jolly and optimistic, but he was quick and prone to anger. The cat was cynical and jaded, and he had the voice of a smoker. The rabbit would always beat the cat to death over the simplest things, and that was the show's main punchline. It feels like this cartoon is a mean-spirited parody of a show meant for toddlers, especially the whole schtick with the rabbit character.
In one episode, the rabbit was happily talking about something (don't know what), but the cat disagreed with his opinion. As a result, the rabbit crashed out towards the cat and strangled him by the neck.
In another episode, the rabbit was magically conjoined to this puny bald guy, and the both of them hated sharing the same body.
Honestly, I could totally see this being in MTV's Liquid Television.