Whenever we've hired a car in Greece we've done it locally once we arrived.
If you want to book in advance here's a link for car hire on Zante - http://www.justzante.co.uk/carhire.htm

We normally hire a car for at least part of our holiday in Greece. In the past I have booked them through the tour company in advance, or sometimes through the rep once we arrive but it's usually just as easy and sometimes cheaper to find a local car ire company one you are there. I have also used these, who are very good and have fully inclusive prices. I believe they operate in most of Greece but I'm not sure whether they are available in your resort.

http://www.economycarrentals.com/

Hi
We have used Economy Cars as well. Their prices are very competitive and I would recommend them.
Enjoy your hols.
Yiamass, Jean

try friends of the ionian. i think it is the cheapest you will find and you also get a free dvd explorer pack with all sorts of guides for the island and a map (costs 9.95 in the shop)
http://www.foi.org.uk/Page.php?page_id=27

We've just come back from Tsivili, and we hired the car from Hertz and collected and returned from Zakynthos airport.

Price was good - and reliable hire company.

The roads leave a little to be desired!!!