YES! I HIGHLY recommend "Amalfi Coast Destination". I have absolutely zero affiliation.
They were recommended to us a number of years ago, when we went to Italy for our first time. Totally independently (and frugally). Rome/Tuscany/Venice/Rome. In Tuscany, we stayed for a week in an agritourismo, and had a rental car for a week.
We were finishing with 4 nights in Rome (after having spent a night there when we first arrived). An aquaintance advised us to use one of those days to do a day trip to Amalfi, and gave us the name of the person she had used -- singing his praises.
So, we arranged it with him. Now the company is a bit larger...
For our one day, we took an early train from Rome to Naples. He met us at the station (sign in hand). We enjoyed a lovely ride in a Mercedes minivan (the height is important to get better views over the railings along the A. Coast). Spotless windows, wearing a jacket/tie, excellent English, and extremely informative.
He drove along the coast (I don't recommend you do it in a rental car -- your eyes will be glued to the road, and won't be able to enjoy the views nearly as much). He dropped us off for some free time in Amalfi and in Positano. A few stops along the way, too, for photo ops. He took us to an out-of-the way restaurant for lunch (on our own), and then to Pompeii. He waited while we had a couple of hours there. We used the RS audioguide to toured it ourselves.
Then he returned us to the train, about an hour before our train (which I think was for about 6:00) back to Rome.
We were quoted a price via email when we were arranging it, and paid cash at the end of the trip (plus a modest tip).
It was such a wonderful experience, that when we stopped in Naples during a cruise, 4 years ago, with a friend who hadn't been there, we did the same trip again. It was a different driver, but just as excellent. He picked up and returned us at the cruise port. Again, it was a highlight of our trip.
It was nice not to have to deal with the potential pickpockets in Naples. Although we carried the cash on us during the excursion, we never felt like that was a problem... you could keep it in a money belt and you'd be fine to access it in the car at the end of the trip. I cannot remember how much we paid, but it seemed like an extravagance the first time... but well worth it. The second time, I knew it would be worth it, and it was.
Good luck!
Cheers,
Vivian