I always use Viator.com for my day trips. If possible look for English-only tours otherwise the commentary will be cut short as they translate in multiple other languages. The tour names are similar but the inclusions and durations can vary so create an account, save to your wish list and compare. You'll need to put in your travel dates to check the availability and price. They will also email you when tours go on sale (usually 10-20% every other week) When one a particular tour's page click on the blue important info tab which will tell you where to meet (airport, train station, city central, etc) and the general schedule for the day and how long you get at each stop (and if any tickets or food is included).
Is the train really not an option? The train from Rome to Naples fast and easy so check the tours from there as well which may allow you some additional options. I find that it is usually a trade-off between the extra cost of the train and the length on time spent on the bus. However, Viator does a good job of breaking up the time with stops and sleeping on the bus back is always an option, I wouldn't sleep on the train unless on a tour. Look for guided train tours as well. The one below and the Florence to Venice day trip that take the superfast train but you have a guide to help you.
**Full-day tour of the Amalfi Coast from Rome* Enjoy a round-trip high-speed train journey from Rome to Salerno Breeze along the Amalfi Coast in an air-conditioned minivan and listen to onboard commentary Visit two of the Amalfi Coast’s most picturesque villages, Positano and Amalfi Make use of plenty of free time to explore at your own pace Small-group tour limited to 10 participants to ensure a personalized experience
Departure point nearby Repubblica metro station, Departure time 8:15am (meet strictly at 8am), Duration 13 hours (approx.) Return to Rome at Tiburtina Train Station at 9pm approximately Price Starts at $215/pp*