We usually go late Sept/Oct or mid to end October and the weather is generally good. Last October we had 30 degrees all week, one rain shower with a bit of wind, but we managed to get in the pool every day and come back with a tan. We are going end Sept this year and were there in June this year (very, very hot it was too!).
The thing about Kefalonia is that the weather can change very quickly and as fast as the rain comes it goes (unless you are really unlucky), I would say that you would be really unlucky to go for two weeks in September and not have mainly good weather. Fingers crossed for you and for us too!
Weather forecast sites always seem to underestimate the temperatures and over estimate the chance of rain so are not necessarily good to use as a guide. Kefalonia is gorgeous even in the rain and it wont be cold. We usually need a light jacket/jumper in the evenings as it can get a bit chilly compared to the day time temps.
Enjoy it and dont worry about the weather. General rule of thumb for us is, if it rains, look in the sky and see where there are no clouds and head there! lol.