You might be better off getting 2 taxis from the rank at the airport, there is always a premium for pre booking
This is the web site of the taxi company www.kostaxi.eu or it might also be worth having a look at people like resort hoppa, if you google Kos airport transfers it brings up a list, we looked a few years back and ended up with the 2 taxi option
We paid 39 euros for a taxi from the airport to Psalidi at 2:30am in the morning. It was cheaper than I expected and because of the time and cost i ended up giving the taxi driver 45 euros.
Don't book as usually more and just go across the road when you leave the airport and ask the taxi drivers :-)