It seems impossible to get a complete set of timetables for local buses but I hope these are of assistance. They are taken from the CTMAM site (Consorcio de Transporte Metropiltano – Área de Málaga) I would recommend you check there regularly for updates.
Most regional buses are run by Portillo Avanza and their timetable is here BUT I advise you to check all times in advance.
Most long-distance buses (coach services) are run by Alsa but the Madrid route is operated by Daibus. For such a small town, Fuengirola is blessed with excellent communication and most parts of Spain are reachable by bus, even if this means changing in Málaga or Marbella, Madrid or Granada.