Just to report back - we used Elephant, who were friendly and efficient. It was an easy pick up and drop off.
We were charged 30 Euro for fuel, but it was about half a tank. We didn't pay cash for the fuel, it was all put on our card.
We drove the car up to Latchi where we were staying and I managed my first Cyprus driving experience ok.
While there we drove up into the hills to the big monastery which was nice. on the way back, the car broke down. In fact the clutch pedal snapped off. We were parked at the time so no harm done. I'm not an expert mountain driver so didn't want to risk any clutchless driving, so I managed to find a signal for my phone and managed to call Elephant. It took a very chirpy mechanic 3 hours to find us, but he did! he brought us a new car and did hat was needed to drive the other back to Paphos.
ALWAYS take a mobile, just in case. Although it was a pain, elephant sorted it out as efficiently as could be expected and we will use them again.