Bob, you can stain or otherwise colour wood to make it black but have you thought about the difficulties of sanding here? There are a few challenges, including the possibility of sanding through the black skin to paler wood beneath but perhaps the main one is whatever the white material ends up being any black dust in its surface could make it look very dingy indeed. And conversely pale dust will be very noticeable in the grain of the black wood. So you'd need a reliable way to clean the surface afterwards if you sand.
Scraping is a better option often when there are strongly contrasting woods present, but I understand manual work like that might not be feasible for you.
...not talking ebony or ivory costs.
How about faux ivory?
What about white plastic? (Don't baulk too quickly, faux ivories are basically off-white/cream plastic!)
Bone? It's been a standard stand-in for ivory since ancient times.
Is it possible to stain walnut for example to get it very dark?
Yes, jet black is easily possible. But you can make nearly any wood very dark or thoroughly black a few simple ways (although a few are tantamount to painting the wood black).
All common methods are surface treatments though, the wood is not coloured through-and-through, so any post-build sanding then becomes a potential issue.
At the moment, I have no supply of maple, is there any way of making beech much whiter?
You can make any wood very pale, nearly white in some cases, using two-part wood bleach.
But can you get that there? And anyway, do you want to mess with strong caustics and concentrated peroxide solutions?
How white is white oak? I can get that but have never used it.
White oak is, er, the colour of oak
It can look very similar to European oak.
I can also get poplar, but am told that does not finish nicely, true or false?
Poplar finishes fine, or at least it can. But it's quite variable in colour and you may have difficulty finding a piece that's uniformly pale.
That statement "wood X doesn't finish well" is usually a bit vague and sometimes (more often than not?) it's more about how much work it takes rather than meaning exactly what the words say. Poplar for example can be made to look a convincing stand-in for cherry, and then finished just the same.