As a tourist, calling the driver you regularly use day or night will not be a problem as that is their job. You can also have the restaurant, bar or hotel contact a driver for you. This applies to the West End as well as the beach road.
Marko,
Living here is different than being a visitor. Visitors don't have usual drivers they call out of the blue. Your usual drivers assume as a resident that you can get yourself around. Visitors are still their priority.
If you need to regularly get around during late or early hours, you need to arrange a schedule in advance with your driver. This way they can adjust their hours for you.