Mike,
Rotax recommends the air cooled engine oil for the 582 because even though its water cooled, its operating temperatures are up in the aircooled engine range. I use Pennzoil Outdoor oil, which meets the standards and is designed for aircooled 2 cycle engines. Pennzoil used to make another oil called Pennzoil Aircooled two cycle oil which just about everybody I know used until it was discontinued. Amsoil and AV oil are also used along with a lot of other brands. They're probably all pretty good. I think as long as you use any well known high temp., low ash oil that meets rotax ASTM/CEC orAPI-TC standards, you'll probably be OK. Oil is a touchy subject with most 2 cycle pilots. Whatever a particular pilot uses is, in his opinion, the greatest thing since sliced bread, and anything else is certain disaster. This is not true of course, and you could probably find several brands in your area that would suit Rotax specs.
Bill.