It is important to note that there are several bushes/trees with similar small orange fruit, all of which can be found in Cyprus (and elsewhere in the E med.) and where they are sometimes confused.
The first is the Mespilus Germanica (known sometimes as the Medlar) which is local to the E Med/Black Sea. http://www.pfaf.org/user/Plant.aspx?LatinName=Mespilus+germanica
The second Crataegus azarolus, a Hawthorn type bush, also known as the Mediterranean Medlar, or Mosphilla. This is apparently the one giving its name to the village just off the highway to Nicosia, Mosphiloti. http://www.pfaf.org/user/plant.aspx?LatinName=Crataegus+azarolus
The Third is Eriobotrya japonica, (the Loquat) which originated in China but has become spread throughout the world, including throughout the Med.http://www.pfaf.org/user/Plant.aspx?LatinName=Eriobotrya+japonica