Melt butter in a medium saucepan over low heat. Remove from heat, and stir in 3 tablespoons water and vanilla.
Combine powdered sugar and milk powder; stir 1/2 cup at a time into butter mixture until smooth. Stir in coconut. Shape into 1-inch balls, and place on ungreased baking sheets.
Chill 20 minutes.
Place chocolate morsels in a small heavy-duty zip-top plastic bag; seal. Submerge in hot water until chocolate melts. Snip a tiny hole in 1 corner of bag, and drizzle chocolate over coconut balls. Store in refrigerator.