'Reasonable', yes, but it is short. Our first trip to Italy a few years ago was 10 nights, and to me that was too short! But you take what you can get, and it will be unforgettable regardless.
So you've booked in & out of Rome Fiumicino, but be forewarned it is huge and not very time-efficient for non-Italian speakers--take my word from experience! Thus, as stated above it's advisable you stay in Rome the night before departure.
As far as itinerary goes, if you have your heart set on Rome, then do it to the max. Stay near either Campo de' Fiori or even Trastevere to get a local flavor, and utilize the Hop-On-Hop-Off bus schedule to get around the city and over to the Vatican. Personally it's kind of a shame you're missing my favorite city, Florence, but there's always next time, and with your guided day trip to Tuscany, you'll get a little taste of it.
RE: the Amalfi Coast, for the beautiful vistas either Sorrento or Positano should be fine. We are finishing an upcoming trip in March by staying 5 nights in Salerno, which is centrally located & lends to day trips to Amalfi, Naples, Pompeii, Paestum without much trouble at all. The key is not to be on the road too much.
This could be a problem if you stay 4 nights in Rome (I'm assuming that your Tuscany day trip will take all day & finishes up back in Rome), then down to Sorrento or Positano the next morning will take a good 3 hours depending on your mode of transport (multiple trains, or bus/hydrofoil). So that would mean only 2 nights there, then you'd have to backtrack to Rome for one night for your flight home the next morning.
Unless...you start on the Amalfi Coast for nights 1-3, travel to Rome on day 4, do the Tuscany day trip on either day 5 or 6, and still have that 7th full day in Rome--your last day should be soaking it all in. Only problem with that scenario is the last thing a jet-lagged person wants after an overseas flight, even if the arrival is 9:30 in the morning, is another 3 hours on the road. But them's the breaks! Like I said, you'll enjoy it no matter what.