How can I adjust the depth to which a pneumatic toilet flush button must be pressed?
If your button is working on pneumatic air, shortening the line or the diameter of the tubing to reduce the total volume of space the gas has to compress into should work. However, air or liquid, I can think of 2 other options:

1) Find a way to increase the air pressure in the lines to just below what is needed to trigger the flush 

2) Add height of your button so you don't have to push it so deep (the travel distance will be the same with this method). Do this by gluing a button right on top of your current one.  If you can't find an appropriate one, metallic one you could measure and design and have one printed using shapeways. Obviously, if you wanted a wood button you could just use a hole saw and some sandpaper and varnish to make your own.