Hi Cheryl,
I'm a mechanical engineer with over 15 years experience in designing, modeling, prototyping and effective manufacturing of different products, ranging from consumer goods to alternative energy systems.
I could design and model your "Air Pong" within 3 days.
I fyou have any drawings/sketches will be kinda useful, even the project is very clear (ID of the cup is accordingly with the ping pong ball, the lenghts(depth) of it is deduced: ball diameter + compressed spring + pushing plate + cca 7-10cm to be able to push the ball with a finger+ accumulators/batteries, etc), still... (in case I omited something).
As for triger mechanism, will be used a common wireless transmiter - I supose you'll make a 3D printed prototype for this device.
What I'll deliver: 3D model and its components in different CAD formats (iges, stl - for 3D printing, step, etc), 3D pdf so you'll be able to open/view the model into the regular Acrobat Reader, and execution drawings.