If 4-stroke then it is possible to use a "steam" engine type eccentric but you need a way to half the amount of times the eccentric moves as you only want the exhaust to open every other rev of the crankshaft. A "Star Wheel" is one method that was used on the early engines, an epicyclic gear box inside the eccentric strap is another. Or you simply need to add 2:1 gearing to drive the exhaust valve and a lobed cam.
The inlet valve is easiest dealt with as an atmospheric one where it is held closed by a light spring and the suction of the moving piston on the induction stroke will pull it open drawing the fuel/air mix with it, again found on most open crank engines so typical of this type of engine.
Star Wheel in action on an Sphinx
Epicyclic gearbox on my Robinson X-type