To be more precise, looking at rain weather statistics of Iceland found at www.weatherbase.com, the less rainy period for the south west area which is the most visited one, seems to be the weeks between March and April and the weeks between August and September (This is valid for the entire south west. Instead if you plan to visit Akureyri area, it seems there will be no problem whenever you go, since the statistics say it is a less rainy place in general).