Preheat the oven to 350 degrees F. Butter and flour a 9×5 inch loaf pan generously.
In a small bowl, whisk together the flour, baking powder and salt. In a large bowl, whisk together the yogurt and the sugar until combined. Whisk in the eggs, orange zest, juice and vanilla extract.
Stir the dry ingredients into the wet, mixing until full combined. Use a spatula to fold the coconut oil into the batter, folding and stirring until the oil is incorporated completely. Pour the batter into the greased loaf pan and bake for 50 minutes, or until the center is set and a toothpick inserted comes out clean.
Let the cake cool in the pan for 10 minutes, then remove it gently and set it on a cooling rack to cool completely. Once cool, pour the icing over top. Let the icing set for 20 minutes, then slice and serve!