I need to make plum colored icing as well as coral colored icing... can you tell me what to use to accomplish these colors?

According to the attached chart, it's violet with a touch of christmas red.
http://www.sugarcraft.com/catalog/coloring/colormixingchart.htm

According to the attached chart, it's violet with a touch of christmas red.
http://www.sugarcraft.com/catalog/coloring/colormixingchart.htm

You are going to have to experiement with this to match any sample colors you might have been given.
Anyone can name a color what ever the want. Just because it's called plum doesn't mean it will be the same shade as a color chart give you.
Yes, a color chart can give you an example to start with but maybe not an actual shade.

Thank you all for your advise

That link is to a blocked site. Try these:
http://www.sweetsugarbelle.com/blog/2011/03/color-chart-and-printing-help/
https://www.candylandcrafts.com/colorchart.htm