I have been trying to find out what to use to pipe a dark chocolate brown design on the side of a cake. Any suggestions on how to get this brown color and what kind of icing I should use?

To me, that looks more like chocolate fondant or modeling chocolate than royal icing.

I'd go with the fondant route. You'll have a very hard time piping that in royal icing and not having it chip during transportation when it's most fragile.

The one thing that you'd have to be careful of is anything staining/bleeding into that satin ribbon around each tier. That's a trickier issue. The wetter or stickier (in humidity especially) your medium, the more likely that is going to occur.

I would use a flower ribbon( they are not satin) they have many different sizes and colors check with florists around, also use glue gun to attach edges of ribbon

Because I didn't get your comments in time, I had to do some experimenting. I actually went with a royal icing that I mixed baking cocoa, and brown and black food coloring. The color came out right on and I didn't have any problems with bleeding or flaking. The design came out almost exactly like the picture. Thanks for your comments!