Stirlingengineforum.com

This is my plans for a near frictionless Stirling engine. This design eliminates the crankshaft and all the torques and frictions associated with it. Energy may be harnessed directly from the main axle and flywheel.

Cordel, I don't think so, sorry. I think the only use for magnets apart from making an alternator is for driving the flywheel on a sealed, pressurised engine such as on of Andy Ross's in his (free down load)book "Making Stirling Engines".
Can't actually see a Stirling Engine in your diagram. The is a rotary displacer Stirling Engine on the net somewhere. Ian S C

If you look at the animation of the free displacer stirling engine you could invent the power piston and do away with the tube. You can also do away with the piston and use a flexible membrane. You had too large an area exposed. You need only the area the size of the tube between the displacer and the power piston (the flexible membrane). The first video shows a balloon as a power piston. At this point you’ll still need a linkage between the flexible membrane and the revolving displacer. The displacer and the power piston (flexible membrane) have to be set to 90 degrees out of phase. Then the rest of your design will work. But there are free piston stirling engines. I have given you a couple of examples. They use air shocks to act as the connecting rod. If you can mimic this in your rotary displacer stirling engine, you can do away with the connecting rod and have a workable engine. Maybe your magnets can be used. Remember the power piston has to be 90 degrees out of phase with the displacer. So, I think you will need to move the magnets from 180 degrees. The single cylinder stirling engine animation shows you why the displacer and power piston have to be 90 degrees out of phase. It’s a pretty simple design, why don’t you build it?
http://youtu.be/IFHdKyVkMbg
http://www.stirlingengines.org.uk/modeng/modl2.html
http://www.infiniacorp.com/howitworks.html
http://www.model-engine-plans.com/engin ... ingbom.htm
http://www.animatedengines.com/stirling.html

I see no reason why this wouldnt work. Even if the moveable plate with the magnets only moves 1mm when the chamber pressurizes, the difference in magnetic force would be substantial. 1/d^2

No. It won't work. The magnets will move to the position of neutral force and stop.