Well... how about making a bunch of dynamic ball entities and setting their physics damage very high, so that when thrown at someone it'll kill them istantly. Then people can run around, pick up the balls and throw them at other people, and that'll also make the balls reusable.
Now, when the game starts, have "entry doors" to the playing field that'll close after a set amount of time, that way, when someone gets knocked out, they respawn behind the door and will have to wait for the next "round" to start before they can play again.
Of course, unless you want a free-for-all dodgeball match, you'd need a Mod to set up the MP game to have teams.
Other than that, it's completely possible.
And while you're modding the source, might as well set up a script function to disable "object pickup" for a player. That way you can have the "field" split into two, and have two triggerzones completely covering each side of the field that will disable a player's ability to pick up a ball if they're on the wrong side.
Great idea, but would take a little bit of work in the source to pull off.
@K RIO:
Hey, just now noticed that you're from Colorado. That's where I live!
I'm around Falcon, what part of Colorado are you in?
The one and only,