Preheat the oven to 375 degrees F. Coat 32 mini-muffin cups with cooking spray; set aside.
Beat the butter and sugar in a large bowl with a mixer on medium speed until light and fluffy, about 1 minute. Beat in the egg, 1/2 cup shredded coconut, 1 tablespoon lemon zest, 3 tablespoons lemon juice and the vanilla. In a separate bowl, whisk the flour, baking powder and salt. Reduce the mixer speed to low; gradually beat in the flour mixture until just combined.
Drop 1 1/2 tablespoons dough into each mini-muffin cup (do not press the dough in). Bake until the edges of the cookies are lightly browned, 12 to 13 minutes. Transfer the pans to racks and immediately make a 1/2-inch deep indentation in the center of each cookie using the back of a melon baller or measuring spoon. Let cool 3 minutes in the pans, then loosen the cookies with a paring knife and remove to the racks to cool completely.
Microwave the white chocolate chips with the cream of coconut in a small microwave-safe bowl in 20-second intervals, stirring, until melted and smooth. Stir in the remaining 1/2 tablespoon lemon zest and 1 tablespoon lemon juice.
Put the remaining 1 1/2 cups shredded coconut in a shallow bowl. Dip the top of each cookie in the melted white chocolate, then dip in the coconut to coat. Return coated-side up to the rack. Dip the bottom of a cherry in the melted white chocolate, then place in the indentation of the cookie. (If the melted white chocolate starts to thicken, microwave again to soften.) Let sit until set, about 10 minutes.
Dropping the dough--not packing it tightly--into the mini-muffin tin helps create a thick, soft cookie.