Preheat oven to 180 degrees C (350 degrees F). Grease a 1l loaf tin and line it with a sheet of baking paper.
In a bowl combine coconut flour, rye flour, baking powder and cornstarch. Stir and set aside.
In a large mixing bowl with an electric mixer beat eggs and the two kinds of sugar until the mixture increases its volume significantly. Add olive oil, yogurt and orange zest (or vanilla extract) and beat shortly at a lower speed, until absorbed.
Gradually add the dry ingredients, mixing gently with a rubber spatula. At the end gently fold in the chopped apricots.
Transfer the batter into the prepared pan and bake for 30-40 minutes or until a toothpick inserted in the centre comes out clean. Let cool for 20-30 minutes before frosting and serving it.