Completely white eyes, I don't know, but I've known two people with icy blue eyes, almost silver, one of the prettiest things I've seen.
As for white hair, I had a friend in grade 1 with natural white hair but not albino. Of course both are caused by melanin deficiency, and you said you didn't want that. However for white any way that's the most effective way, and mind you, all three people mentioned were tanned, not albino.
As for black eyes, they exist, they are rare but they exist and they are from excessive amounts of melanin. Basically really really dark brown you could say that doesn't count but you wont get any closer.
One thing about your question doesn't quite make sense: you want 'common and natural ways' when those hair and eye colours are not common and mutation is a natural occurrence (red hair and blue eyes being mutations ie. blue eyes are from not producing enough melanin after birth, in which most babies have blue eyes).
that being said, if we use mutations an deficiencies, we can achieve your proposed colours. since there can be yellow/golden parts in irises (mine for example) it could be assumed that mixing of yellow and green could make light green. the golden part is caused by aging, and is only a ring around the pupil so i guess it still doesnt count.
the other thing that factors colour in eyes is light refraction, if the structures were 'weird' enough, you could have iridescent irises if you wanted. some blue eyes look violet in the right light. the same goes for hair, if you had hair that say, had microscopic holes in it that refracted the light like the blue morpho butterfly's wings, mybe you could have strange coloured hair at the right angle.