In a food processor, finely grind the pistachios. Remove 1/4 cup of the ground pistachios and set aside.Add the pitted dates and 1/2 cup of the shredded coconut to the food processor and blend well until the mixture sticks together. Using clean hands, form the mixture into 1-inch balls, roll them in the remaining coconut or pistachios and set on a platter.
To make chocolate date balls, remove half of the blended date/coconut mixture from the food processor, then add 2 tablespoons of cocoa powder and process until well blended. Roll in additional cocoa powder to resemble chocolate truffles.