I'm so sorry I didn't respond sooner.. I only now saw your question.
If your ship is in at 7AM, assume you can be on a train to ROME by 8 to 8:30 AM (check the train schedules to be sure in FTROUTE's post on train travel in Italy.) It is about an hour trip into Rome. Then from Rome termini station go down into the Metro (access is in the front of the Termini station) If you didn't buy a combination train and metro ticket in Civ - a BRIG ticket(you can do this and its cheaper), you can purchase the all day Metro/Bus ticket there. Then take the metro to the Vatican station. Its about a 15 min walk from the metro station to the Vatican. So all in all a 10:30 tour is about right. Maybe 11AM would give you more time provided the train schedule from CIV has an 8 or 8:30 train you are in great shape. The latest I would want to leave CIV to make 10:30 is 9AM and that would be tight.
If you don't buy a BRIG ticket in CIV, be sure to by your return trip ticket when you get to the termini station in the morning so that you know you have seats on the return train. If you are taking the commuter type train there are no reserved seats so this is not a worry.
I would leave Rome no later than 5PM to be safe.
That should give you plenty of time at the Vatican an possibly the coliseum if you want to see that also.
Carnival Cruise Lines:
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