Put the white chocolate in a large bowl.
Add the heavy cream to a heavy-bottomed saucepan and warm it over very low heat. Put the white chocolate into a bowl and pour in the hot cream. Whisk until all of the chocolate has melted. Add the butter and whisk until the mixture is smooth. Refrigerate the ganache for 1 to 2 hours, just enough to be able to form it into balls.
Use a tablespoon or small scoop to measure even amounts of ganache into small balls. Put the balls on a parchment or silicone mat lined sheet tray. Refrigerate for 1 hour to firm up before the next step.
Melt the dark chocolate in a double boiler (or a microwave). Dip each ball in the melted chocolate (2 forks make it easier to fish out dipped chocolate balls). Put the coconut into a medium bowl and add the ganache balls. Toss to cover them in the coconut, then put them on a wire rack over a parchment lined tray to dry. Allow the truffles to set for about 10 minutes before devouring.