Preheat oven to 350 degrees. Fill 12 muffin cups with liners.
In medium bowl, beat 1/2 cup butter until smooth.
Add sugar and beat until fluffy and light.
Add eggs one at a time, beating well after each.
Add vanilla and beat well.
In small bowl, mix together flour, baking powder, salt and cream of tartar.
Add dry ingredients and milk to the butter/sugar mixture, alternating each and stirring well after each addition.
Evenly distribute batter between muffin cups.
Bake at 350 degrees for 18 to 20 minutes.
While cupcakes are cooling, make the icing by combining butter, Key Lime zest, vanilla, salt, powdered sugar, and Key Lime juice and mixing at low speed until consistency desired, adding 1 to 2 Tablespoons milk if needed.
Ice the cupcakes when they are cool.
Top with yellow coconut.
Decorate as desired.
Serve and Enjoy!