Thanks for the replies.
There are many threads on these three options: FCO to Rome, Rome to Civitavecchia, and Civitavecchia to FCO. My problem was not finding much on FCO to Civitavecchia.
I finally found a couple of limo/private transfer services, but they were extremely expensive, like in the $180 range. We are considering just going from FCO to Rome City Centre and staying a couple of days. We've been to Rome a couple of times and have seen a lot of the sites, but there are a couple we haven't seen yet, like the Colosseum underground tour.
We do love Rome as it is a most fascinating city! So, we're kicking around the idea of just seeing some more of Rome. Our cruise doesn't happen until April of 2025 so we have plenty of time to think about it. :^)