1) Appeal to all age groups, but especially kids. You can make it educational and fun at the same time. For example, throwing any object involves the laws of physics, so tie in knife throwing to the physical properties governing the process. Mention records set in the sport and how difficult or how much skill it took to acomplish the feat. Discuss how throwing knives (hatchets, axes, etc...)differ from regular knives and why. Also, tie in the history and legends surrounding the sport and the famous folks who have enjoyed the hobby.
2) For the parents and adults, emphasize how it promotes (or should) safety, discipline, concentration, and hand-eye coordination. All skills that will benefit other areas of your life
3) Promote it as a sport and not a fighting skill. Darts are widely accepted, but have their origin in combat/hunting.
4) Make it hands on. It was mentioned earlier and I totally agree. I got hooked on knife throwing by trying it and hearing that nice little "thunk" as the blade stuck. Make it a 'gimme throw into stryrofoam or the like so most folks can do it.
5) Create or use a scored target and make a game out of it. Like darts only harder and better outside
6) Hold exhibitions during county fairs, reenactments, rodeos, etc. Use plenty of fun (balloons, playing cards, bottle caps, moving objects) targets and events (blindfolded throws, long distance throws, little knife and big knife or hatchet throws) that will wow the audience and show how fun knife throwing can be. You will get plenty of interested folks and maybe a few new members to the KTA.