Red icing is probably the most difficult to make. I love AmeriColor's Super Red gel paste coloring! It doesn't take as much to get a nice red and doesn't have the off-taste like some others (Wilton).
All icing will darken over time and while drying, but it is especially true with red. Try to make your red icing at least a day in advance, cover with plastic wrap, pressing down onto the icing, cover and refrigerate. Bring to room temperature before using and just give it a stir.
When making red, aim for a little lighter than you'd like on your final product. Believe it or not, the icing above turned into a perfect, bright red on my cookies. If the icing is a true, deep red before it goes on the cookies, it can turn extremely dark once dry...close to black. (If your icing is too dark, stir in some white.)
Red icing can also change in high humidity. If it's humid and you notice your cookies getting splotchy once dried, don't panic. The icing will eventually even out in color.