Are you talking about tear stains or pigment? The yorkie eye is suppose to have black pigment around it almost like eyeliner. If your talking about tear stains, there are many reason that dog's eyes tear, from food allergies, to teething to genetics. This link has some good information on the causes of excessive tearing and how to treat the stains.
Tear Staining: The Causes & Cures
I've never heard of an all white Yorkie either, is it registered with the AKC? White dogs, such as the Maltese, do have more problems with staining.