In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar and beat until fluffy. Add milk and vanilla and beat well.
Add flour and beat until well mixed. Stir in cherries and pecans. Divide dough into thirds. Shape each portion into a 7-inch-long log. Roll each log in 1/4 cup of the coconut to coat. Wrap and chill in the refrigerator at least 2 hours or up to 24 hours.
Cut into 1/4-inch-thick slices. Place on an ungreased cookie sheet. Bake in a 375 degree F oven for 10 to 12 minutes or until edges are lightly browned. Cool cookies on wire rack. Makes about 80.