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What is an average internal psi for a medium sized piston stirling engine? Iam thinking of using a pneumatic drill motor instead of a piston. The pneumatic motor will run 1800 rpm at 90 psi. Pneumatic tools have high torque. Maybe this is the way to increase the torque of a stirling engine.

Your air motor won't work, A piston in place of the diaphragm will. If you double the heat (Kelvin) you will double the pressure, so the atmosphere is near enough to 15psi. Zero C = 273*K add the ambient temp, say 20*C = 293*K x 2= 586*K = 30 psi.
To run the air motor, you need a continuous air supply, and a high volume of air, the average home handyman air compressor has a hard job keeping up with the amount of air required. Ian S C

Ian SC
You stated the pneumatic drill needs continuous pressure at all times. It would receive its highest pressure when the displacer was rising. As in the U-tube video below the air blower only fires when the one high spot in the cam comes around. The drill motor would only fire (be triggered) Once every cycle of the displacer. A one way pressure valve opens at high pressure. The flywheel keeps the engine turning not the drill motor. Would having the working gas be helium or hydrogen and pressurized make the drill motor perform better?

http://youtu.be/plJG5ZMHK10

The main problem (discounting the pulsing pressure) is the volume of air required, one of those little air motors puts out at least a HP at normal working pressure, and to allow for inefficiencys , conciderably more power would be needed to power the air motor. Ian S C

Just been looking at the air requirement of small pneumatic motors; .5 hp 6 - 10 cfm
1 hp 12 - 15 cfm
1/4" Die Grinder 4 - 6 cfm
Screwdriver 1 - 6 cfm
Normal average pressure 100psi. This is just a small selection of the smallest tools. Ian S C