Cream together the butter and sugar in an electric mixer or by hand.
Add the eggs and vanilla and beat until fluffy.
Mix together the flour, baking soda and salt.
Add to the shortening mixture and stir or mix together thoroughly.
Stir in the rolled oats and the coconut.
Shape the dough into 2 rolls, each about 2 inches (5½ cm) in diameter.
Wrap in baking parchment or wax paper and refrigerate for at least 4 hours or overnight. The dough may also be frozen at this stage.
To bake, preheat the oven to 350°F (175°C).
Slice the dough in ⅓ inch (about 1 cm) slices. (If the dough has been in the freezer you may need to let it thaw a bit so you can slice it more easily.)
Bake on ungreased baking sheets for 10 minutes or until lightly browned. If you are baking the dough from frozen the cookies may take 11 to 12 minutes to bake.
Allow the cookies to cool on the pan for a few minutes before carefully removing to a wire rack to cool completely. They do taste lovely warm, but if there are any left, be sure to store them in an airtight container.