Camel

Try this board. I asked a taxi quesiton last year and got a reply within 24 hours.

http://www.agni.gr/message_boards/display_forum_topics.asp?ForumID=30

We've taken taxi transfers from the airport to Agios Stefanos (a couple of miles south of Kassiopi) for 50 euros. I suspect you can negotiate a cheaper deal if you really feel the urge.

Time should be around 35-45 minutes - depending to an extent on how long it takes to battle through Corfu town.