Heat oven to 350 degrees. In a large bowl, whisk flour, cornmeal, coconut, baking powder, and salt.
In the bowl of an electric mixer fitted with the paddle attachment, mix eggs, sugar, oil, and zest on medium speed until well combined. Reduce speed, add flour mixture, and mix until just combined. Fold in cherries and pistachios.
Transfer dough to a parchment-lined baking sheet and pat into a 14-by-4-inch log. Bake until firm and golden, 30 to 35 minutes. Transfer to a wire rack and reduce oven to 325 degrees.
Once cool, transfer log to a cutting board and, using a serrated knife, cut diagonally into 1/2-inch slices. Arrange slices on parchment-lined baking sheet and bake, rotating halfway through, until just golden around the edges, 15 to 18 minutes. Let cool completely.
Biscotti can be stored in an airtight container up to two weeks.