Here is a list of events for June to August 2009, in Cyprus. All information  are from http://www.carnaval.com/cyprus/

"Kataklysmos" - Festival of the Flood (June) Limassol

Kataklysmos is a festival which takes place near the sea shore of Limassol, on the Sunday of the Pentecost and the Monday of the Holy Spirit. It is unique in its kind and has a paganistic character.   We don't know for certain what the origins of this festival were. A lot of  people believe that kataklysmos originated from the ancient ceremonies in honour of Aphrodite and Adonis. The custom of throwing sea, river or lake-water at one another has prevailed both in areas near the sea and inland of Limassol.   On Sunday and Monday, a variety of dance and song competitions take place.  Popular songs known as "chatista" are sung by different singing groups which complete each other.

Shakespearean nights (June)

The Shakespeare festival is a charity event annually organized by the Society for Chest Diseases at the ancient theatre of Curium.   There, Shakespeare’s plays are staged, in a fascinating environment in the open air theatre of Curium. The performances attract large audiences from Cyprus and abroad.