Low power, low performance stepper motor
If you are happy enough with unidirectional motion, you could hack the mechanism from an analog quartz clock. They will operate from 1.5V pulses and draw perhaps 10mA in short pulses. 

100mA is definitely on the high side for any kind of coin battery. 



If you are willing to go to two batteries in series, there are small bipolar (4-wire) steppers used in GM (General Motors, not Genetically Modified) automotive instrument panels. The coils draw about 20mA @5V  and incorporate a gear train. 1mm shaft diameter. They fail so often that plenty of replacements are available on the aftermarket.