Preheat oven to 350 degrees F. Line 9 muffin cups with muffin liners or spray with nonstick cooking spray.
In the bowl of a stand mixer fitted with the paddle attachment, beat together butter, sugar and lemon zest until light and fluffy. Beat in eggs, one at a time. Beat in cream until combined. With the mixer on low speed, mix flour and salt until just combined. Stir in 1/2 cup coconut and gently fold in blackberries.
Spoon batter into cups, filling the cups, and smooth tops. Divide batter equally among prepared muffin cups. Top the muffins with remaining 3 tablespoons of coconut. Bake until muffin tops are golden and springy to the touch, 23 to 25 minutes, rotating halfway through baking time. Cool muffins in muffin tin for 5 minutes, then transfer to wire rack and cool 5 minutes before serving.