We would like to see Cinque Terre on our cruise stop in Livorno in April. My husband wants to rent scooters but I think it might be too far for that. Is it easy to get to the train station from the cruise port? Any suggestions/ideas would be appreciated.

I've done some research on this in the past and found lots of information about this on Trip Advisor. Here is one of the threads that might be helpful:

http://tinyurl.com/b9tz4eu

I am assuming that you want to do a self guided tour at Cinque Terre. Cars are not allowed there so options would be limited if you are not physically able.

Taking the train will limit your time available at Cinque Terre. How mcuh time you have at port? If you do not want to take the ship's excursion, then you should look into hiring a private guide.

Most private tour would take you to one end, drop you and the guide off, and then pick you up at the opposite end.

I wouldn't chance and rent a scooter in a foreign place when you don't speak the lanuage or understand the signs.

The ride from Livorno to the 5 Terre is pretty long doing that by scooter. The easiest thing, I suggest you, is like we did: we booked a driver picking us up in front of the ship who drove us to the 5 Terre area in about 1.40 hrs.
The drive is smooth except the mountain drive after Portovenere but it was outstanding: we could visit 3 villages of the 5 since the time at our disposal during our shore excursion were just 9 hours. The view overlooking the villages was amazing and totally worth the money we spent.
We made the reservation through: www.shoreexcursionsinitaly.net and that was the best way to get there in such a short time available.