We present the results of our systematic investigation of the RE dependency of superconductivity in the parent compounds T′-RE2CuO4 (RE=Pr, Nd, Sm, Eu, Gd, and Tb). Superconductivity with a transition temperature (Tc)≥30K is achieved for RE=Pr and Nd by the metal organic decomposition (MOD) method. By contrast, Tconset is at highest 20K for RE=Gd. A stringent control of synthesis- and post-annealing-conditions is required to obtain superconducting films. Our results indicate that the induction of superconductivity into T′-RE2CuO4 cuprates strongly depends on the RE3+ ionic size. This trend is discussed from the viewpoint of RE-dependent thermodynamic stability of T′-RE2CuO4. For smaller RE3+ ions, the thermodynamic boundary conditions become tighter.