I agree with early morning.
I was always up at the drink station very early getting coffee for myself while the rest of the family slept. Each morning, the Mickey Pool was being refilled - so the water is clean and the pool appears to get drained and cleaned each night. Moreover, the pool was pretty uncrowded from opening until about 10am or so.
On port days - CC day or any other port day - the pool stayed pretty uncrowded all day long.
We found embarkation day to be medium crowd levels.
On sea days, I'd look to the Navigators to find something else to keep the kids occupied from 10 or 11ish until the next morning - the pools do empty out around 6:00pm (first dinner seating), but the water is a little gross. See what movies are playing in the afternoon, see the matinee of the stage show, or do some of the other activities on the ship.