Evidence: Shaun of the Dead, Zombieland, Dead Set and that Simpsons halloween episode with zombies.
Working backwards: The Simpsons halloween episode had only two funny bits. The moment when Homer gunned down Flanders, and everyone assumed Homer knew Flanders was a zombie, when in fact Homer just gunned him down because he hated him. The moment when the zombies - who in this confused take on the myth craved brains rather than just human flesh - ignored Homer because of his lack of brains.
Similarly, the more recent Simpsons take on 28 Days Later worked well because it was a very effective piece of brutal storytelling. But funny? Hardly. Not that it matters - The Simpsons has been so funny so often that it can afford to do something other than comedy from time to time.
Dead Set - a genuinely horrific TV film with zombies more akin to the ones in the remake of Dawn of the Dead. I neither knew nor cared who the "real" people were in this - stars of "reality" TV, apparently - but I was delighted with the subtext: anyone who watches "reality" TV is ipso facto among the ranks of the undead. But funny? Again, not really.
Zombieland. Not really a zombie film, as the monsters are simply diseased. They're no more zombies than the infected in 28 Days Later. There's an "unserious" vibe that runs throughout the film, which includes the rather tedious "twist" of the tough hero doing anything for a twinkie, and there's an overlong cameo by An Actor Playing Himself that really doesn't work. It's easy to see how it was intended as a comedy, but it's never really funny.
Shaun of the Dead. I suppose the trailer was quite amusing, and there's a nice sequence where Shaun goes to his local shop and completely fails to realise there's a zombie apocalypse going on. But as my brother observed, "I was expecting to be hurting from laughing. Instead, all I could manage was a couple of chuckles." Maybe it works better for people who aren't very familiar with zombie stories.
Which brings me to my theory. Anyone who finds themselves immersed in zombie movies will at some point have come up with their own spoofs. The more scared you were by the real movie, the more imaginative your jokey response. And if you're so steeped in zombie movies that you've even watched the really terrible films - Zombie Diaries, for instance - then your mind cannot help but create even worse mickey-takes.
In short, no zombie comedy will ever match up to your own imagined undead laugh-fest.