We present an optimization algorithm for the design of multilayer antireflection (AR) coatings for organic photovoltaic (OPV) cells. When a set of available materials for the AR films is given, the proposed method allows for searching the globally optimized AR structure that maximizes the short-circuit current density (J_SC) under simulated solar light illumination (AM 1.5). By applying this method to an OPV solar cell with a configuration of Al/P3HT:PCBM/MoO₃/ITO, we demonstrated that J_SC can increase by 7.5% with a 6-layer AR coating, consisting of MgF₂, ZnS, and Al₂O₃. A notable feature of this method is that it can find not only the optimal solution, which maximizes J_SC, but also the quasi-optimal solutions, which increase J_SC to nearly maximum levels. We showed that the quasi-optimal solution may have higher robustness against deviations in film thicknesses, from their designated values. This method indicates the importance of practically useful, non-optimal solutions for designing AR coatings. The present method allows for extending the user's choices and facilitates the realization of a practical design for an AR coating.