On our Med cruise this past May, someone on our Cruise Critic roll call arranged for multiple vehicles and drivers with
RomeInLimo (
www.romeinlimo.com) from Civitavecchia and Naples. From Civitavecchia - we went to Orvieto instead of Rome, because we spent 3 days in Rome pre-cruise. We toured Pompeii, Sorrento, and Positano from Naples. RomeInLimo isn't cheap (~ 90-100 euros pp) - but they do a great job.
To make private tours more affordable for a few people - arrange to share tours with others on your cruise meets thread.
**To the OP - make sure you know whether your tour price includes entrance fees - particularly to the Vatican. RomeInLimo's prices don't include entrance fees.