ZOMBIEPOCALYPSE RPG just won't suffice, you need an alternative. One such option is Zombie Dice, from the venerable Steve Jackson Games.
Nominally this is a "party game", although I can't imagine anyone playing this at any of the parties I go to. It does make for a convenient "pick-me-up" game, for when you and a few friends have a half hour to kill. Involving nothing more than a handful of dice and the included dice cup, all you need is a flat area to roll the bones.
The rules are fairly simple; roll the dice and keep track of the results. You take on the roll of a hungry zombie chasing after the Living, and the dice you roll decide the outcome of your chase. Each die has a three symbols on it, indicating whether you caught somebody (a brain), if they outran you (feet), or if you took a bullet (shotgun blast). The idea is to roll as many brains as you can while avoiding the shotgun blasts; take three shots and your turn is over. The dice are differently colored; the red dice have more shotgun blasts, while the green more brains (the yellows dice are neutral). Each turn, you roll three die at random; you keep going until you chose to stop or you get 3 shotgun blasts (at which point you lose all the brains you accumulated that turn, adding to the risk). The game is over once a player collects thirteen brains.
The game is largely luck-based, and most strategy boils down to ending your turn after you roll your second shotgun blast. You can choose to press your luck, but that rarely ends well (more often you just get three shotguns and lose any brains you rolled that turn) so is only a tactic worth using at the very beginning or very end of the game. The game is not particularly deep and so does not have much longevity, but on the other hand it is very easy to learn, the rounds are fairly quick and it's a fun way to pass a few minutes.
Steve Jackson Games also offers two expansions, which add special dice to the pool (including a 12-side "school bus" die), but the added complexity does little to better the game. The dice are decently made and the dice-cup is a nice addition to any gamer's collection, even if it isn't used to play Zombie Dice. You can also download the game as an app for the iPhone or a Windows phone, and there is a demo version available on the web using Flash. These give you an idea as to the mechanics of the game work, but it isn't the same as playing it with a bunch of friends.
Zombie Dice isn't the greatest of games, but it is quick, easy-to-learn and fun in short bursts. It includes 13 dice and a dice cup, and has a suggested price of $13.13 (notice the recurring 13 motif). Personally I think it is just a bit overpriced for what you get, but barring that problem, it's a decent enough title and worth picking up by any zombie-loving gamer.