I'm a regular flyer to Bombay. As others have said, there are frequent flights from the domestic terminal to Goa and Jet Airways is by far the best choice of carrier.However, note that flights from Europe get into Bombay between 10:30 PM and 1:30 AM and the first flight to Goa isn't until around 6 AM. You might want to spend the night at the Leela Hotel which is right by the airport and is a pretty good hotel.

The best connections are via Paris, Frankfurt and London Emirates doesn't (IMHO) make sense because you have to make an extra connection in what is already an uncomfortably long trip.