I'll be renting in Cyprus too.
What did you find in terms of additional required insurance? I called up Hertz & they said that there was no need for additional insurance (like in some countries, such as Italy, where additional insurance is required by law). I called up GEICO, whom I have standard car insurance with, and they told me that they only cover rentals in the US & US territories.
I called up Amex & they said they only act as secondary car insurance (I asked them if that meant that it would be primary insurance since my personal insurance didn't cover as primary - the person said it would only be secondary - secondary to what? I ask - secondary to the purchased insurance - yeah, right...they don't know what the hell they're talking about).
I also called up Visa - who said they'd be primary insurance covering losses & damages as long as the rental is paid in full with the Visa card - here's a link to info on their page -
http://usa.visa.com/personal/cards/b..._personal.html