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Most of the existing stability analysis methods are capable of determining the oscillatory stability of black-box converter interfaced generators (CIGs) under given operating conditions only but can hardly identify the critical operating conditions. In this letter, an oscillatory stability region (OSR) is defined with the short-circuit ratio and output power as variables, and a method to obtain the OSR for the black-box CIG is proposed. First, the CIG is modeled as a variable-operating-point impedance model (VOPIM) through perturbation tests. Then, the critical operating points, for which the CIG system has a zero-damping oscillation mode, are determined by VOPIM-based oscillatory stability analysis so as to obtain the OSR. Finally, the accuracy of the OSR is verified through control hardware-in-the-loop tests. The OSR is of significant meaning for the control strategy and operation plan optimization of the CIGs. [ABSTRACT FROM AUTHOR]