Sorry, no photo op today as I can't find the little servo motor I was going to use.
Anyway, I suggest a servo motor or as Jim B suggested get a motor (gear head motor for reduced RPM and torque) and run it like a piston on a crankshaft. A Google of Robotic Motors should be a good start. Robotic sites should give you more ideas. That would be my thinking on how to go about it anyway.
Have a look at the attachment, a four bar linkage.
Crank #1 is rotated by the motor.
A linking bar connects crank#1 to crank#2.
Crank #2 pivots about the rod at the bottom end.
The distance Radius1 is smaller that Radius2.
As the motor turns, crank2 will move in an oscillating angular motion about it pivot point.
Anything attached to crank2 near the pivot point will flap up and down.