We're staying near the airport the night before and had booked a ship transfer from the airport to the cruise port that left at 11:30. However, I just changed the trasnsfer to one leaving from tronchetto at 9am so that we could get to the ship earlier. Just call Royal, they will explain the transfer options for you. You can transfer from the airport, the "city center" which I think is Piazalle Roma, or from Tronchetta.
Our flight doesn't get in until 7:30 on Saturday, so I think we're just going to look for something by the airport.