Whenever I need to replace riveted equipment or whenever I add new equipment I use 316L SS screws, bolts and lockwashers. It's handy in case I need to replace, change my mind, upgrade, etc. I don't think there's anything really special or advantageous about rivets. The manufacturers use them because it's faster assembly and much, much cheaper than stainless fasteners and some places are just plain hard to access to get a wrench on the nut.
Check your fasteners for tightness once in a while through the season. If you're spooked by a nut coming loose you can always use a couple of nuts; one tightened down to be locked against the other one. I've never had to do that but it's an option where vibration and high load may be present.
Sooner or later, though, you will be faced with mounting something in a place where only a riveter will be the way to fasten.