is there an icing that is better for a coconut cake, and that you can decorate with ( basket weave)

I use 7-minute frosting for coconut cake. I cover the entire cake with flake coconut, so there's no decorating involved. I'm guessing from your post that you are planning to decorate the sides of the cake with basketweave and then just put the coconut on top of the cake? I have eaten coconut cakes iced with buttercream before and they are yummy (I just prefer the 7-minute frosting as it is more traditional where I live). Since you are wanting to do a basketweave design on the cake, I would just use your favorite BC.

I use cream cheese with a little coconut extract and it is delicious. There is a decoraters cream cheese iciing in the recipes

I flavor IMBC with Malibu- it's heaven!