We realize bistability in the spinor of polariton condensates under nonresonant optical excitation and in the absence of biasing external fields. Numerical modeling of the system using the Ginzburg-Landau equation with an internal Josephson coupling between the two spin components of the condensate qualitatively describes the experimental observations. We demonstrate that polariton spin bistability strongly depends on the condensate's overlap with the exciton reservoir by tuning the excitation geometry and sample temperature. We obtain noncollapsing bistability hysteresis loops for a record range of sweep times, [10 μs, 1 s], offering a promising route to spin switches and spin memory elements.