Not sure where to find a chart. We were there last June. Average temperature--hot (90's) but with a nice breeze. Rained off and on one day only. Actually felt hotter in October because there was less breeze.
Did you check out the weather on this website? You can probably email someone for more detailed info! There is a Hurricane season Junish to Novemberish, although it is a hit or miss situation usually. http://www.ambergriscaye.com/pages/town/weather3.html Weather is day to day, climate refers to monthly/annual patterns of weather, might try this site also. Belize it!
June is beautiful too, VERY hot and humid. Usually not much rain unless an unusual hurricane season that starts early right. (though that is technically when it starts and usually most action is in Aug, Sept, Oct)