Is there some kind of trick to keeping black icing in it's place....it always runs out onto my white icing and turns it a pick/purple color.

I think you are referring to color bleeding, rather than the icing running. There are four things that I have found to be very helpful in preventing dark/bright colors from bleeding.

(1) First off, use a high-quality food coloring, like CakeCraft (I'm sure others can suggest some other good brands), look for "Super -" in the name. You won't have to use as much to get a good color. Wilton colors are only good for pastel-medium shades; terrible for black and red.

(2) Color you icing the day before, and stop when it is a shade or two lighter than you need. It will darken considerably after it sits awhile, so you end up adding less color.

(3) For black, start with chocolate icing and you will not need to use nearly as much black coloring.

(4) Use royal icing instead of BC; it will almost never bleed.

Here are my tips.
As was said before, start with chocolate icing. Make it a dark gray, not black. Every color of buttercream will darken after it crusts. Dark gray will turn black after it dries. The biggest mistake that I see people make is using way too much coloring in their icings.

Also, I wait for the under color to crust and dry, usually an hour or more before putting black on top. I always have this problem when making eyes. I make the white part of the eye and wait for it to dry, sometimes overnight if I can and then add the black part of the eye.

I have found that all buttercream icing colors will bleed after 1 to 2 days.

Thanks so much for the advice! I will try using chocolate icing and royal icing

'How do you stop black icing from running?'
Take away its running shoes!

Ok, but seriously, are you keeping your cake in the fridge then bringing it out to serve? As cakes come up to room temp colors will run...