"Doorskins" would be a good material, and probably the stuff monophoto was talking about. It's a tropical hardwood plywood, looks something like mahogany but isn't (sometimes marketed as "Philippine Mahogany").
If any plywood is properly varnished you won't have to worry about it delaminating. If it is properly dried when it is varnished it is most unlikely it would be dimensionally unstable.
Real ebony is very rare and expensive. There is some wood out there marketed as ebony which is simply black wood, or a wood stained black. Not to say it wouldn't work, whatever it is.
Any of the plywoods mentioned would work if they are the right thickness, and 1/8 inch is fairly common. And they can all be stained before varnishing to look reddish so they won't clash with the mahogany or cherry.
p.s. I disagree with Stan's comment re the plywood. Plywood is much more stable than a single layer sheet of wood.