Amalfi Coast Tour from Rome by high speed train

You are looking for a day tour of the Amalfi Coast with Rome as your origin?

More exactly, Shorty, what sort of tour are you looking for? Can you give us more details?
You understand that very little of A.C. is served by train, and that the ferries aren't running to most coastal locations in March either?

Take a Freccia high speed train to Naples, then a commuter Circumvesuviana train to Sorrento or to Meta.
Once there catch a SITA bus to Amalfi. A stop in Positano would be nice.
Once in Amalfi, I would take another SITA bus to Salerno. That way you covered the entire AC.
From Salerno you can take a high speed train back to Rome.
It’s going to be a long day and in March days are short (daylight savings in Europe starts the last Sunday of March), therefore if you want to cover all of that you should leave from Rome as early as possible in the morning. Just getting to Sorrento is going to take almost 3 hours once everything is said and done. The bus ride from Sorrento to Salerno along the Amalfi Coast is almost 3 hours, even if you make no stops to visit Positano and/or Amalfi.
Last high speed train to Rome departs from Salerno at 6:48pm.
But there is also a slightly slower Intercity train departing at 7:37pm (takes 3 hours instead of 95 min with the Freccia train however),

The wise Roberto is stating logistically what you would have to do to accomplish this in March, but I don't think he is recommending it. Yes, the Amalfi Coast in March has few tourists and not everything is open, but it is spectacular--in good weather. Don't even try this in rain or wind, which is likely at times in March.

If you just want to 'see' the A.C., take the Freccia train from Roma Termini station through Naples to Salerno, then the SITA bus an hour to Amalfi. If you wanted to see Positano as well, you'd have to change buses there, and another 30 minute ride. Then retrace your steps. A long-a** day...

Maybe better--and only if the weather's OK--would be to take the Freccia train to Naples (1 hr 10 min), switch right there to the Circumvesuviana train, about 25 minutes to the Pompei Scavi stop and tour the ruins for 2-3 hours, then backtrack, maybe even stopping Naples for some pizza. Still a long day, but doable.

Enjoy your planning!

How long are you going to be in Rome? Where else are you going? Is seeing the Amalfi Coast a priority for you or just something you heard about as something you might do? Cause depending on your circumstances the obvious answer is to try for at least one night. Then it's a very rushed but 'doable' side trip. Doing it all in one day in March you aren't going to see much of anything and spend a LOT of time in transit. The problem with scheduling one night there though is you'd probably want to schedule it in advance and then if you got a rainy couple of days it would be worthless.

Thank you all for your help! We realize it will be a full day, but it is something we really want to do on either a Friday/Saturday while we are in Rome. Unfortunately our schedule does not allow us to stay overnight at the coast.

Please think twice, then think again, before you do this. As Roberto has laid out, it's a lot of schlepping, and in my opinion, you don't get much.

I saw Sorrento and Positano as a day trip from Naples. I consider it one of my biggest "travel mistakes." These are places to be settled into, not seen on the fly. I felt it was a waste of a day. If I had come all the way from Rome instead of Naples, I'd have been really upset.

Definitely, if you are determined to do this, check the weather that morning first. There really is no point in going if it's not nice.

If you absolutely must go, I’d recommend to go to Positano and back, only.
Amalfi is 50 minutes further.

The Frecciarossa from Rome to Naples takes 70 min, and the first departs at 7am (that’s the one you should take if you really want to do it). There is two Freccia every hour on average, plus some slower trains.
The Circumvesuviana commuter train from Naples to Sorrento takes also 70 min (one every 30 min) and from there the bus to Positano takes 40min.
Once you factor in transfers and waits, you need about 4 hours to get to Positano. If you leave at 7am you can make it by 11am.
Have lunch and enjoy Positano for a few hours after that.
You MUST take the 4:40pm bus (at the latest) back to Sorrento to arrive on time to Naples for the last Frecciarossa to Rome, departing Naples at 7:30pm.
There are some trains departing after that but they are slow Regionali or night trains.

Amalfi is further down the coast. You can’t visit both Positano and Amalfi in a day in March. Technically you could but you’d have very little time to see either before making it back to Rome with public transportation. Maybe if you hire a driver in Naples you could. But the cost would be much higher.