Thanks to Alanya and Antalya Airports it is easy to come to Alanya all year.
Alanya-Gazipasa Airport is only 40 km to Alanya and there are flights to İstanbul and Ankara everyday. Also there are direct international flights to many countries in summer and also in winter.
Alanya-Gazipasa Airport flight information website: http://www.gzpairport.com/
Antalya Airport is 130 km to Alanya and it is a bigger airport operating both domestic and international to many countries all year.
Antalya Airport flight information website: http://www.antalya-airport.aero/
It is also possible to come to Alanya by intercity busses from all cities of Turkey.