What would happen if a diamagnetic material is placed within a capacitor, instead if a dielectric material?
All these materials, to my knowledge, are good electrical conductors. Which means that you've just replaced your capacitor by a sequence of metal-conductor-metal junctions. In other words, a resistor. It's not a capacitor any more.

For extremely high frequencies, where the dynamic EM field within the diamagnetic material plays a role, this will have very interesting effects that can be better described by microwave components such as circulators, isolators, but your question shows no hint of you being at this level of understanding, so I'd recommend doing a little more material science/physics/RF theory homework first, before approaching these components.