I'd put a coil in the stick, wound over ferrite rod or a string of ferrite beads, and detect the effect on the coil of eddy currents in the ring when it is placed on the stick. For example, use the coil as part of the tuned circuit in an oscillator, and adjust the gain of the oscillator so that putting the ring on the stick stops it. Then use a diode/resistor/capacitor to detect the output of the oscillator and feed it to an analog input pin.