The whole year is around 30°C (90°F) at day time and around 25°C (77°F) at nights. The shore water is normally around 29°C (84°F) degrees. There may be a short cool down in January. There is the rain and hurricane season from May till October. For Barra not much to worry, it rains usually at nights, and the hurricanes are less frequent and strong as in the Caribbean. So if you consider climate it doesn't matter when you want to be here.
The place gets really crowded with Mexican tourists from December 25 till January 5, and also in the two weeks surrounding Easter Sunday. Further there will be a lot of people around May 5 (1862: Fall of Puebla (end of French occupation)) and September 16 (1810 Independence Day (end of Spanish occupation)).
The best month to be here is November. Everything is still green, and it is before high season.