We study the linear diamagnetic response of a superconducting cylinder coated by a normal-metal layer due to the proximity effect using the clean limit quasiclassical Eilenberger equations. We compare the results for the susceptibility with those for a planar geometry. Interestingly, for R similar to d the cylinder exhibits a stronger overscreening of the magnetic field, i.e., at the interface to the superconductor it can be less than (-1/2) of the applied field. Even for R >> d, the diamagnetism can be increased as compared to the planar case, viz. the magnetic susceptibility 4 pi chi becomes smaller than -3/4. This behavior can be explained by an intriguing spatial oscillation of the magnetic field in the normal layer.