In a large bowl, cream butter and sugar until light and fluffy.
Beat in water and vanilla.
Combine flour, oats and salt; gradually add to the creamed mixture and mix well.
Shape a tablespoonful of dough around each cherry, forming a ball.
Place 2 inches apart on ungreased baking sheets.
Bake at 350 degrees for 15 minutes or until bottoms are browned.
Remove to wire racks to cool.
In a small bowl, combine the confections sugar and enough milk to achieve smooth dipping consistency.
Dip cookies, then roll in coconut. Place on waxed paper; let stand until set.
Makes 3 dozen.