I have a client who wants a wedding cake with buttercream that he wants to have the color of burgundy, as he says "deep red". Any thoughts on where to begin? I want to try to avoid artificial colors. Any formulas on the tried and true reduced beet juice?

use poudered food coloring.

Use powered food coloring... I repeat! I've tried everything and it is the only thing that makes a good deep color without a disgusting flavor or change in consistency.

Use powdered food coloring!

yeppers

Where can one find powdered food coloring? All we have in local stores is paste or liquid (ugh!)

check out places like: http://www.pinenose.com/prfoco.html
http://www.sugarcraft.com/catalog/coloring/powdered.htm
http://www.candylandcrafts.com/powderedfoodcoloring.htm

candy makers and bakers mostly use them.
check out the nice blood red at candy makers.