Difficulty calling Trenitalia?

I suggest looking at the train schedules for a Venice to the CT trip and consider a non-sleeper trip. The trip normally takes 5.5hrs to 6.5hrs depending on which trains you are on. There are EuroNight (EN) trains that route through Milan and Bologna but these are places where you will change trains in the middle of the night. Sleepers are normally traveling in a north/south direction. For example, one of the sleepers in the evening that is available to you in Venice begins in Taravisio on the Austrian and Slovenia border and terminates in Rome. You transfer in the night in Bologna and then transfer again in Parma. I'm betting that these transfer trains in Bologna and Parma are not sleepers. I see the one from Venice to Genoa. You change trains in Milan. The second train is a regional and not a sleeper. Where is your destination in the CT? Are you staying in the CT or nearby? I could link you to train schedules if I know if you need to come into the CT from the north or the south.

The phone number on the Trenitalia customer service page only works for calls made from within Italy. I don't know of a way to call Trenitalia from outside Italy.

There is a direct Venice-Genova night train which leaves Venezia Santa Lucia at 22:51 and arrives at Genova Piazza Principe at 05:05. From there you can go to La Spezia and then on to the Cinque Terre. If you can't complete the booking on the Trenitalia site, you could try booking at www.italiarail.com.

Tim is correct, the one he quotes above does go through to Genova without changing trains. I looked at several but missed this one.