While there no longer are direct night trains from Switzerland to Rome, you still can travel overnight if you're willing to make some connections.
There is a night train that leaves Milano Centrale at 23:20 and arrives at Roma Tiburtina at 07:30.
Leave Interlaken Ost at 19:01, connect in Spiez and Brig, and arrive at Milano Centrale at 22:35 in plenty of time to catch the night train.
Or leave Zuerich at 19:09 on a direct train to Milano Centrale which arrives at 22:50. It's a shorter connection, but you'll have enough time to catch the night train.
If you book well in advance (up to 90 days) on the Swiss Rail site, you can get a discount fare around 30 CHF for either Interlaken-Milano or Zuerich-Milano.
It can be difficult to impossible to book advance discount tickets on the Italian Rail site because it doesn't like certain non-Italian credit cards (US cards, for example), but there is no harm in registering on the site and seeing if you can complete the booking process. If that doesn't work, you can book the night train on the Swiss Rail site.