"October to May" is the answer everybody gives and it hides most of what you want to know. The diving inside that window is not uniform, and the month you pick changes which sites are realistic.
October and November
The monsoon is letting go. Visibility is still recovering - fifteen metres is a good day early in October and twenty-five by late November. Fewer people, lower prices, and a genuine chance of a blown-out morning. Good value if your dates are flexible.
December to February
The peak, and it deserves to be. Flat seas, thirty metres of visibility on the offshore sites, water at 28 degrees. It is also when the boats are fullest and the marine park permits go quickly. Book two months ahead.
March and April
Our own favourite. The crowds thin, the water warms to 30 degrees, and the visibility stays excellent. Manta sightings, such as they are here, cluster in this window.
May
The last usable month. Hot, still, occasionally spectacular, and the pre-monsoon weather starts making the long crossings unreliable in the second half.
June to September
We do not run trips. The southwest monsoon closes the marine park, the offshore sites are unreachable and the shallow sites silt up. Anyone selling you Dixon Pinnacle in July is selling you a boat ride.