Hi again,
Oh ok, well then that should make it simpler (the magnetically active coins).
It could be that the permeability of the core you are using relatively too high. In other words, if the u of the core is 5000 a small change may be hard to detect, but if the core was more like 500 it might be easy to detect. Try using a lower permeability core and see if that helps. If you can you might even try an air core, and if you can have the coin pass through the center of the coil.
Another idea is to have one coil on top, the other on bottom, the top coil is the drive coil and the bottom coil is the sense coil. The coupling between coils should increase when the coin is passed between them.
Another idea is to have the coin pass between a good magnet and a linear hall effect device. The HED would detect some nominal magnetic field without a coin, but once a coin is introduced it would cause a higher level field to be detected by the HED, which would respond by putting out a larger or smaller voltage level. Two HED devices might be able to detect different diameters as different outputs in the two.
You can try passing the coin side ways with flat faces toward the HED and magnet, and you can try passing the coin up right where the diameter creates a stronger link between magnet and HED device. Different diameters should produce a different field level.