To get you pointed in the right direction:
(1) go to www.trenitalia.com/en/index.html
(2) Put in Rome as your departure station (this will get all trains departing from Rome)
(3) Put in Civitavecchia as your arrival station
(4) From the list, pick a train near your desired time and click on 'Details'.
(5) Click on the train number to get the detailed schedule for that train. It will show arrival/departure time if that train hits your desired schedule.