Overnight Train from Rome > Prague

Not sure if a night train is the answer to what you need if you are trying to save time. Budget carriers like Smart Wings offer inexpensive & quick transportation. In many cases it is cheaper to fly with them than to take the train. Last time I looked the flights with Smart Wings one way from Rome to Prague are as low as 52 EUR per person and about 2hrs flight time.

There is a CNL leaving Roma Termini @ 19:05 and arriving in Munich hbf @ 06:30 with no train changes. I would suggest you visit Munich and then take a train from Munich to Prague using a Bayern/Barvarian ticket which is for 2 or more people traveling together. Link: http://www.bahn.de/i/view/USA/en/prices/germany/laender-ticket.shtml. There is a direct train that departs from Munich Hbf @ 09:01 and arrives @ Praha (Prague) @ 12:18. I may add it may be less expensive to fly to either cities than taking a night train.

www.bahn.de/i/view/USA/en/index.shtml, the German Rail site given by JB, is the best site for detailed timetables for virtually all of Europe. After you get summary timetables for Roma-Praha, click on "Show details for all" to see the connecting points. You'll see that to get to Praha at 12:18 requires leaving Muenchen at 07:19 and connecting to a bus in Nuernberg. (The direct train that leaves Muenchen at 09:01 doesn't arrive in Praha until 14:58.) If you do separate advance bookings (up to 92 days allowed) on the German Rail site for Roma-Muenchen and Muenchen-Praha, you can get very good discount fares. A Bayern-Ticket will only get your group from Muenchen to the Czech border. You would need a Bayern-Boehmen-Ticket to get the group to Pilsen. From there you would need to buy regular tickets to get the rest of the way to Praha. As JB said, it can be cheaper to fly. Your budget airline choices for Roma-Praha are Wizz Air and Smart Wings.

A night train that trip will save you no time. Better take a flight instead.