In the heatproof bowl of a stand mixer, whisk together egg whites, sugar, salt, and cream of tartar. Place bowl over a saucepan of simmering water, and cook, stirring frequently, until sugar dissolves and an instant-read thermometer registers 160°F (71°C), 5 to 10 minutes.

Carefully return bowl to stand mixer. Using the whisk attachment, beat at high speed until cooled, about 10 minutes. Reduce mixer speed to medium-high. Add butter, 1 tablespoon at a time, beating until combined after each addition. With mixer on medium-high speed, add melted coconut oil in a slow, steady stream; beat until mixture thickens and comes together. (Frosting may look curdled at first, but keep beating and it will come together). Beat until frosting is smooth. Use immediately.