There are strict rules to whitewater slalom, which you can reveiw by visiting the ICF (International Canoe Federation). These rules regulate kayak size, kayak equipment, and many other things.
Slalom Kayaks are not designed for anything other than competition. They are simple in design, but made of very high quality materials. They are not easy to control and should not be used recreationally. Here is an image of a slalom kayak from KayaksPlus.com

Slalom Kayaks are often hard to find, so here are some manufacturers of slalom kayaks which you may refer to: Galasport,
iTomco,
Nomad