Probably December-April, because they are drier and a bit cooler. August and September also experience a drop in rainfall, with warmer tempertures of course. You have an excellent chance of good weather any time of year. There is a small risk of hurricanes in September and October; however hurricanes rarely go there.
Here are links to average rainfall (in mm) and average high temperature (in C) for various sites in the Dominican Republic, including Punta Cana.
http://www.activecabarete.com/info/images/weather-precipitation.gif
http://www.activecabarete.com/info/images/weather-temp.gif
For an overview, read
Active Cabarete: Climate in the Cabarete region
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