The sloshing of liquids in microgravity is a relevant problem of applied mechanics with important implications for spacecraft design. A magnetic settling force may be used to avoid the highly non-linear dynamics that characterize these systems. However, this approach is still largely unexplored. This paper presents a quasi-analytical low-gravity sloshing model for magnetic liquids under the action of external inhomogeneous magnetic fields. The problems of free and forced oscillations are solved for axisymmetric geometries and loads by employing a linearized formulation. The model may be of particular interest for the development of magnetic sloshing damping devices in space, whose behavior can be easily predicted and quantified with standard mechanical analogies.