Duathlon generally means run-bike-run. Biathlon means ski and shoot, but I have seen events that were labeled biathlon where people bike-run. It is gererally hard to find events with a swim that are not triathlon. I don't think many people are interested in swim events (as in, people who are not competitive swimmers and don't compete in that capacity). It can also be very tricky for a race director to find a nice body of water that is safe for an event. Plus you have to hire lifeguards to work the swim portion of the race. This is why duathlons are ever so popular. You can sometimes find paddle-bike-run triathlons where you use a canoe or kayak instead of swimming. I have yet to see an event (in WI) where you swim-bike or swim-run.

If you want to make up your own event, make sure you do the swimming first for safety sake.