I've found the most common woods used in American-made player piano
action pneumatics to be poplar, basswood, and sometimes maple
(Gulbransen built nearly the entire stack out of maple).

Much of the rest of a Standard stack is made of red gum, a very
soft but fine-grained wood that is easily sealed for airtightness.
Red gum was also commonly used for much of the Ampico mechanism parts
as well as the unit valves: the stack tier chests are made of maple,
and the pneumatics are of poplar or basswood.

The downside of red gum, due to its softness, is that screw holes
are easily stripped out of it, and it's easily crushed under spring
pressure (again, think of those Ampico solid "springs" that leave
their mark on the valves).

I've rarely seen mahogany used in early actions of various kinds.
The laminated woods used in bellows and pumps are often basswood or
poplar, but I have seen maple, birch, or chestnut (usually just for
the middle ply).

John M Runge