Rome to Capri to Amalfi Coast, back to Rome in 2 Days

You can take the ferry from Capri Island to Amalfi. Than take the bus from Amalfi to Positano and to Sorrento. From Sorrento take the local train to Naples. From Naples take the train back to Rome. But the boat service only running on weekend from Easter to mid-June. That mean you might have to take the boat from Capri to Sorrento. From Sorrento, you can take bus or taxi. The boat from Capri to Sorrento take about 45 minutes. Bus from Sorrento to Positano take about one hour. From Positano to Amalfi take about 50 minutes.
You can check out the boat schedule www.metrodelmare.com The train from Sorrento to Naples take about one hour. The fast train from Naples to Rome take about one hour 20 minutes. The slow train can take up to 2 hour and 45 minutes.

Thank you. Instead of taking bus from Sorrento to Naples. When I arrive Amalfi, can I travel to Salerno and take train back to Rome. I note there is some speed train departing from Salerno, and would that be a better option?

Part 1: You can go by bus to Salerno from Amalfi. You'll see the blue buses near where the boat comes in. Not sure what "visiting the Amalfi coast" means to you. Your current itinerary will use most of 2 days getting to/from Rome & Capri. Day 1 is to Capri. Day 2 From Capri by boat to where? From that town are you planning to just ride the bus or do you plan to get off along the way? If so what are you doing with your luggage? (If you stay the night of Day 1 in Capri you won't be able to effectively use the hotel's luggage storage on Day 2 to sightsee.) Also, you don't want to drag your luggage around Amalfi coast towns.

Part 2: Or Day 2 you could take a boat from Capri to Positano (or Amalfi), tour, stroll, eat & spend the night. Next day take the ferry/bus to Salerno and catch the fast train to Rome. Or to experience the views, take the bus to Sorrento (sit on the left side) then catch the Sorrento bus to Rome or train. If you stay in Positano (& don't/can't take the ferry) ask your hotel what time you should catch it- some buses skip Positano if they are full. Don't know that this would be an issue in May. I stay in Positano & since my 1st trip have used the Rome-Salerno & return fast train. Love the ferry to/from Salerno to Positano & along the coast but it doesn't run a full schedule in May is gets "interrupted"/suspended for bad weather, especially after noon. For a first time trip to the Amalfi coast, the road trip between Positano & Sorrento is an experience worth having- spectacular views. From Sorrento sit on the right side of the bus; to Sorrento from Positano, sit on the left. If you don't want to spend the night but still want to at least see the coast and one town. Sorrento may have a luggage storage so that you could boat to Sorrento, store luggage, see Sorrento/eat & take the bus to Salerno (or the train to Naples then Rome). If you take the bus, there is a simple change of bus usually in Amalfi. Obviously taking the boat to Amalfi is a faster route to Salerno than taking the boat to Sorrento then bus to Salerno.

Bessie, Yes, it will be a better option to go to Salerno and take the train.
Since you only have one day. I suggest take the ferry from Capri to Sorrento and go south. Go early in the morning. Also the buses in Amalfi Coast are crowded and no room from luggage.

Bessie, You might want to consider to stay in Sorrento for the night instead of Capri. Sorrento have better night life and you can take off early next day.
Kong Hei Fat Choy

Thanks for advice from Rick and LaVee.
I will put my luggage in Rome before I head to Naples, just pick 1 day necessities. For Day 1, since I'd visit Blue Grotto, I plan to stay 1 night in Capri in case I cannot catch evening ferry to Sorrento (believe early May is not peak season, so the schedule may be scattered and few). For Day 2, my schedule is somewhat like Capri->Sorrento->Amalfi->Salerno. To enjoy the scenic, would take bus from Sorrento to Salerno (interchange at Amalfi). My worry is schedule too tight for Day 2 and I cannot get train from Salerno to Rome.

Don't know if you saw this or not, but in it RS gives helpful info. I'd seriously consider staying in Sorrento and day tripping to Capri. http://www.ricksteves.com/plan/destinations/italy/naples-sorrento-amalfi-coast.htm