Preheat oven to 375 and line cookie sheets with parchment or silicone baking mats.
Put butter and both sugars in a mixing bowl and beat until fluffy. Add eggs one at a time and beat on medium speed until blended in.
Place flour, oats, coconut and baking powder in a separate bowl and mix with a whisk until combined. Add to mixing bowl with the butter mixture and mix until blended.
Add milk and vanilla extract to the bowl and mix one more time.
Place dough by rounded tablespoons on cookie sheet, about 2 inches apart. Sprinkle a little cinnamon sugar on each cookie and bake until golden, about 15 minutes.
Cool for a few minutes on the cookie sheet and then remove to a cooking rack to cool further.