Janfred is correct. I tried to access the first post in this section that has a link to a train travel guide by a past member. However the link did not seem to work.
I would say that if you can get the express train (not the commuter train that stops at every station along the route) that the train would be faster than taking a private car. AND far cheaper. The train stop in the main station in Rome and you can quickly get into the subway right there at the train station in Rome. In Civ. its a couple of blocks to walk from the port bus drop off point to the train station. When you buy your ticket for Rome ask about the all in one ticket for the train/bus/ subway (metro) you can then use that for the day and get around really easily.
You can also go to the train Italiania web site to check schedules. Click on the little British flag to read it in English. You should also be able to purchase tickets on the website but it may be wiser to wait until you arrive so you know for sure when you will be there. There are ticket machines in the Rome train station (again click on the British flag fro English) I would buy your return tickets when you get to Rome so you know you have seats AND you know when you need to be back at the train station. Leave yourself some wiggle room time-wise and you should be fine.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013