We have used this company for nearly 40 years. They speak english and have a “desk” (more like a van) at Alicante airport.
http://www.solmar.es/carhire/javea_car_hire.shtml
Again, a local company, been around for years,
ABOUT JAVEA
http://en.comunitatvalenciana.com/places-to-visit/cities/costa-blanca/xabiajavea
The official Tourist Board site. Check out the fiestas and other events, there is usually something happening around the area.