There are several bus companies with which you can reach the airport, whose timetables vary depending on the company. That is why we refer to the most common one, Buses Portillo.
If you take the bus from Marbella station it takes approximately 45 min to get Malaga airport.
Taking the bus from Málaga Bus station it only takes 11 minutes. You can check the timetable following the link.Buses timetable
In the Costa del Sol there is only one railway line, the commuter train, its route goes from Malaga to Fuengirola in a round trip, pay attention to advises to stop at Malaga airport.
If you take the train from Fuengirola station it will take 30 minutes to arrive.
Taking the train from Málaga station only takes 11minutes. You can check the timetable following the link.Train timetable