The assumption of asymptotic flatness for isolated astrophysical bodies may be considered an approximation when one considers a cosmological context where a cosmological constant or vacuum energy is present. In this framework we study the motion of spinning particles in static, spherically symmetric and asymptotically non-flat spacetimes with repulsive cosmological vacuum energy and quintessential field. Due to the combined effects of gravitational attraction and cosmological repulsion, the region where stable circular orbits are allowed is restricted by an innermost and an outermost stable circular orbits. We show that taking into account the spin of test particles may enlarge or shrink the region of allowed stable circular orbits depending on whether the spin is co-rotating or counter-rotating with the angular momentum of the particles.