Localized states are found in many pattern forming systems. The aim of this paper is to investigate the occurrence of oscillatory localized states in two-dimensional Boussinesq magnetoconvection. Initially considering an idealized model, in which the vertical structure of the system has been simplified by a projection onto a small number of Fourier modes, we find that these states are restricted to the low ζ regime (where ζ represents the ratio of the magnetic to thermal diffusivities). These states always exhibit bistability with another nontrivial solution branch; in other words, they show no evidence of subcritical behavior. This is due to the weak flux expulsion that is exhibited by these time-dependent solutions. Using the results of this parameter survey, we locate corresponding states in a fully resolved two-dimensional system, although the mode of oscillation is more complex in this case. This is the first time that a localized oscillatory state, of this kind, has been found in a fully resolved magnetoconvection simulation.