In a medium bowl, cream together the butter, white sugar, and brown sugar until light and fluffy. Beat in the eggs one at a time, then mix in the peanut butter. Combine the flour, baking soda, and salt; blend in to form a soft dough. Mix in coconut. Drop dough by teaspoonfuls onto ungreased cookie sheets. Flatten each cookie using the tines of a fork.
Bake for 12 to 15 minutes in the preheated oven. Cool on wire racks.