Near-infrared transitions of the monoanion and monocation radicals of buckminsterfullerene isolated in argon matrixes (C-60(+/-)/Ar) have been investigated using magnetic circular dichroism (MCD) and absorption spectroscopy, over the temperature range T = 1.6-30 K and magnetic-field range B = 0-4 T. Structure in the origin-band regions of both ions is partially attributed to the occupation of inequivalent matrix sites. The origin bands for the H-2(g) <-- H-2(u) and (2)G(g) <-- H-2(u) transitions of C-60(+)/Ar are nearly coincident, with the former at higher energy. The ground-state orbital angular moment of both ions are quenched by crystal-field-stabilized Jahn-Teller (CF-JT) effects. Trapping is strong for C-60(-)/Ar but weak for C-60(+)/Ar. The transition from static to dynamic CF-JT effects for C-60(+)/Ar gives rise to unusual temperature and magnetic-field dependencies of the MCD.