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A direct current (dc) voltage biased II-VI semiconductor multiquantum well structure attached to normal contacts exhibits self-sustained spin-polarized current oscillations if one or more of its wells are doped with Mn. Self-sustained current oscillations are due to repeated triggering of charge dipole domains at the magnetic wells and motion towards the collector. Without magnetic impurities, the only configurations appearing in these structures are stationary. Analysis and numerical solution of a nonlinear spin transport model yield the minimal number of wells and the range of doping density needed to find oscillations, the current-voltage characteristic curve and the main features of stable stationary and time-periodic states. Our study could allow designing the oscillatory spin-polarized current injectors.