Welcome to the forums, B!
If determined to do this, I would definitely look at tours which get you most of the way there by high-speed rail thus cutting significant time, although you'll likely spend 2+ hours each way on the train. The bus tours eat up additional hours on the road that could be better spent sightseeing Rome. As Christine mentioned, Walks of Italy/Take Walks has a smaller-group (max. of 18) tour to/from Rome and Salerno by fast train + around the coast by ferry. It isn't offered every day, and costs.$293.49 CAD pp. I haven't taken this one but this is a highly reputable company that has seen many, many recommendations for their tours on the forums over the years. Personally, I wouldn't try to cut corners on an all-day tour that has to cover this sort of distance, and a private tour for just the two of you from Rome would be VERY expensive.
https://www.takewalks.com/rome-tours/amalfi-coast-from-rome-day-trip/?tap_a=29793-20da11&tap_s=246785-b1586d
This tour runs rain or shine, and if the sea is too rough to dock in Positano, they'll use ground transport to access that town. You don't mention wanting to see Pompeii so if that's the case, you'll need a different tour. I wish we knew what your larger itinerary looks like? There is a LOT to see in Rome so hope you're not cutting it short to do this tour. Also, your Venice post indicates that you're wanting to book $ 70 CAD hotel rooms during high season, and that concerns me too.
To add: most of us recommend booking with the tour companies themselves versus a 3rd party re-seller like Viator. If something goes wrong, it's best not be working through a middleman.