Mumbai to Goa!Goa Jan Shadabdi Express
If you are looking for a day train to Goa from Mumbai, the Mumbai Goa Jan Shadabdi Express (Train No:12051/12052) is a comfortable option. You'll need to start quite early though (leaves Dadar station by 5.25 AM ).
The next probable morning train option is the Mandovi Express (Train No:10103/10104) that leaves Mumbai CSTM at 7.10 AM, and also with many more stops enroute than the Goa Jan Shadabdi Express.
Jan Shadabdi got 2 coaches of AC Chair Car (Class Code : CC) and the rest of 12 Non AC Sitting type (Class Code : 2S) coaches.
Also note, these trains are operated in the Konkan Rail Route, which has a monsoon timetable. During the monsoon period trains typically has an early stary, that's to compensate for the slow speed through the mountainous Konkan route during the rainy season.
AC Char Car should cost you around Rs1000 and the 2S ticket about Rs300. Check it out at the official IRCTC website for schedules,seat availability and online reservation
Stops from Mumbai to Goa : Dadar –>Thane–> Panvel –>Chiplun –>Ratnagiri–>Kankavli –> Kudal–>Thivim–>Karmali–>Madgaon.
The train earlier used to operate up to Karmali station of Old Goa. There are over 10 other train options from Mumbai to Goa