The following newspaper article reports on a new Saigon to Tuy Hoa train service.
http://en.vietnamplus.vn/new-railway-se … /96548.vnp
The article says the service takes between 12 and 15 hours, leaving Saigon Railway Station at 21.25 and arriving at Tuy Hoa Station at 17.25 the following day.
Note: This is a period of TWENTY hours. Passengers will find it more convenient to travel up to Nha Trang on faster train, then change to the 0620 local train to Tuy Hoa, arriving around 1100.
I couldn't find mention of the local train on the VN Railway's webpage, but it does indeed exist and makes one complete round trip each day, leaving Tuy Hoa at 1400 and arriving in Nha Trang between 1800 and 1900, depending on how often it has to stop to let the express trains go by.
Light meals and cold beer are available, hard seats (non-aircon) or soft seats (with aircon). For the best views sit on the eastern side of the carriage.