IMO, the result you see is due to the fact that the nickel coating is acting as a shorted turn resulting in the lowered inductance.
Pm
Good point, Partzman! Not only the nickel coating is conductive, but also the NdFeB, and therefore as you say such a core constitutes a conductive loop like a shorted transformer secondary. If i1 is the current in the coil and i2 is the current induced in the magnet causing a field that opposes that of i1, a voltage U applied to the coil is such that : U = L*di1/dt - M*di2/dt where M is the mutual induction coefficient. The equivalent inductance L' is therefore such that L'*di1/dt = L*di1/dt - M*di2/dt so L'= L - M * di2/di1. As di1 and di2 are proportional, di2/di1 is a positive constant depending on the transformation ratio and the resistances of the inductor and the loop constituted by the magnet, So we have L' < L. ... So it seems my Nickel coated Neo magnet increases coil inductance. 
Gyula
This is also true! As neodymium and nickel have a permeability > 1, they increase the inductance, while the shorted secondary loop effect decreases it. So we have two antagonistic phenomena that will give opposite results depending on their parameters. I think that in your case, the effect of the permeability dominates because the core fills the coil better than the ball magnet in my case, so the effect of the increase of the permeability which increases the inductance takes over the effect of the coupling which reduces it. So we have L' > L. The devil is always in the details  The lesson I learned is that the magnetization of the magnet plays no role. Only the permeability of the medium and the possible couplings leading to currents in the core, play on the inductance. By using a copper tube as a core, I predict that the inductance will decrease significantly.
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