I'd absolutely avoid any rubber backed carpet.

The rubber will rot and be a mess to take care of when it does.

On a pontoon boat I'd use exterior grade plywood, seal it with epoxy on both
sides, screw it down to the stringers and lay the carpet. I might even get a
little fancy and use snaps to install the carpet so I could take it up once in
a while or even after a washdown. I believe you can get epoxy at a BOAT/US or
West Marine store.

Butch