Since infomation on duck egg colors seems to be really hard to find (i.e. I couldn't even find it last time I did a google search; I had to search through my old bookmarks), I thought I'd share this webpage: http://www.runnerduck.net/egg-colours.php.
They talk about the black eggs, as well as blue/green and white eggs, and the genetics behind the blue/green versus white eggs. Here's one quote
The colour is laid down in the thick, calcium-rich testa of the shell. The pattern tends to be in the cuticle, the outer protective layer. It is only in the later stages of the egg’s passage along the oviduct that the markings are applied by pigment-secreting areas of the uterus. I imagine a sort of spiral production line with little paint guns firing at given intervals. If the production line is quite fast there will be streaks or elongated marks. If it is slow, there may be round spots or even bands.
And, a pretty picture showing some of the different colors:
If you have any more info about duck egg colors and what causes what, such as what causes the brown or black "bloom" (is that the right word?) on the egg shell, please share!