Recently I do some design on Eink and due to the special fresh mode on Eink screen most of the interface is only black and white even without any gray. So perhaps it's a way.
Since eink design is also lack of research, at least I find nothing. I conclude some of my own.
Layout is 1st place:
Color sometimes can destract the eyes and the make people ignore the layout problem. and now only black and white may call for more attention on the layout, font size and weight to make web balanced. And sometimes this kind of simplism can be beautiful.
Making sure button can be clicked:
Clickable button can be missed when colors are gone. You can use underline or obvious button style to make sure users' notice.
Try the styles that fit for black and white:
Some styles are very suitable for black and white, for example the handwriting, doodle, geometric and some oldstyle things. So It can be tried to combine the elements.
It's hard to do all things only black and white. Try to persuade clients, or treat it as a challenge :) it can be fun.
I like the web design of Remarkable(an eink brand). Though its web is not only black and white, it may give some inspire.