Good luck on finding any color except black or white. I have seen other colors, but they are hard to find.
The picture of the "Pinto Woolies" are made with plugs. You cut out a circle from the back side and replace it with a different color angora. You have to sew in the plug from the back side. I make my miniature pinto woolies this way.
As far as dying angora, I have not done that before, but I have dyed Islandic Sheep with Rit dye (Orange) and it worked pretty well. Made the skin a little stiff when it dried though.
Hope this helps a little!