I'd use black fondant - premade, commercial fondant.
I agree with leah... buy it.... it's the best way to have true black.... then steam it... and it will be perfect.... good luck
looking at the picture it looks like buttercream to me, to many small "imperfections" to be fondant.
But I agree with the above, buy black Satin Ice fondant. If you insist on making it, then do NOT kneed in the color, add it to your liquid ingredients before adding in the powdered sugar, a lot less color, and a lot less kneeding.
If your customer doesn't want fondant ask her/him if it's ok to use chocolate buttercream. The chocolate helps with the taste! I use AmeriColor, Super Black color gel. Color the icing a dark gray and let it sit over night, it will darken to a nice black. I don't like using the Wilton black gel, it takes too much and it leaves a bitter taste. Hope this helps.