With baking powder.
Compare the version from the March 13, 1879 from the Goshen (Indiana) Times:
Coconut Cookies. — Two cups of sugar, one cup of butter, one cup of butter, two eggs, one teaspoonful of soda dissolved in one tablespoonful of milk, one large coconut, grated, and enough flour to roll it out.
From the box of A.D. from Lutz, Florida, by way of Pennsylvania in the 1940s, and originating in Ohio in the 1920s.
1/2 c. butter
1 c. sugar
1 beaten egg
1/4 c. milk
1/2 c. coconut
2 c. flour, and
1 teaspoon baking powder.
Roll thin, sprinkle with coconut and bake in quick oven.