I agree with the comments above. June will be less crowded and the bigger or less visited islands obviously offer you the best chance of 'quiet'. However, you need to balance that with your interest in diving.

Not all islands offer diving. Diving is strictly regulated in Greece and only allowed in certain areas. For example, diving is available on Rhodes but only in one location(Kalithea Spa bay) and only through an authorized dive company boat. Also bear in mind that nowhere in the Med is really that great for diving. Fishing has pretty much removed the fish and the coral throughout the Med.

I would suggest you research what diving is available as a first step in picking an island. Then worry about where to stay on that island to avoid the bulk of the crowds.