Coconut oil doesn't fully absorb into the skin. This makes it great as a treatment product, but not great for daily wear. I would not recommend using it before applying makeup.
Go to the store and buy some. You can't really make this recipe without one of these essential ingredients. Other oils don't harden well so they can't really be used...
Cooking oil is not good for the skin and may cause a breakout. Coconut oil works well in this case because it easily moisturizes the face and has molecules small...