Hi BT. You'll have to get yourself to Malaga on the Saturday for the service bus to Granada, as the only buses heading out of Fuengirola to that destination (as far as I know) are on day excursions.
The buses are on the hour from 7am at Malaga's main bus station at Paseo de Los Tilos and journey time is 90 minutes. Lots of buses available on Sunday night as well (see link).
I'd take the train from Fuengirola to and from Malaga. Heading out, the service is six and 36 minutes past the hour (first train 6.36), and, back, two and 32 past the hour (last train 22.32). Make sure you use Malaga Renfe station to drop you off near the bus station and not Malaga Centro (also confusingly known as Malaga Alameda).
You can, of course, opt to go to Paseo de los Tilos by service bus from Fuengirola. As far as costing goes, prices are similar, just a shade faster by train. You choose!
http://www.estabus.emtsam.es/