We spent a day in Kefalonia about 10 years ago while we were doing a yacht cruise of the Ionian Islands. It is one of the larger islands in the chain, and unlike many of its neigboring islands, Kefalonia has a pretty large population. There are taxis on the island, but not nearly enough to handle a large influx of cruise passengers. If you want to take a private tour, I think your smart move would be to try and contact a local taxi company (or tour company) on the internet and prearrance your tour. You do not mention your cruise ship name, but this island is in an area that is seldom visited by larger ships. The Ionians are a major area for yachting and smaller boats (the region is charming) but other than Corfu, few of these islands have facilities for large cruise ships.