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The interplay between superconductivity and charge density wave (CDW)/metal-to-insulator transition (MIT) has long been interested and studied in condensed matter physics. Here we study systematically the charge density wave and superconductivity properties in the solid solutions Zn1-xCuxIr2-yN(N = Al, Ti, Rh)yTe4. Resistivity, magnetic susceptibility and specific heat measurements indicate that the CDW state was suppressed immediately while the superconducting critical temperature (Tc) differs from each system. In the Al- and Ti-substitution cases, Tc increase as y increases and reaches a maximum around 2.75 K and 2.84 K respectively at y = 0.075, followed by a decrease of Tc before the chemical phase boundary is reached at y = 0.2. Nevertheless, Tc decreases monotonously with Rh-doping content y increases and disappears above 0.3 with measuring temperature down to 2 K. Surprisingly, in the Zn1-xCuxIr2Te4 solid solution, Tc enhances as x increases and reaches a maximum value of 2.82 K for x = 0.5 but subsequently survives over the whole doping range of 0.00 - 0.9 despite Tc changes slightly with higher doping content, which differs from the observation of zinc doping suppressing the superconductivity quickly in the high Tc cuprate superconductors. The specific heat anomaly at the superconducting transitions for the representative optimal doping samples are all slightly higher than the BCS value of 1.43 and indicate bulk superconductivity in these compounds. Finally, the CDW transition temperature (TCDW) and superconducting transition temperature (Tc) vs. x/y content phase diagrams of Zn1-xCuxIr2-yN(N = Al, Ti, Rh)yTe4 have been established and compared, which offers good opportunity to study the competition between CDW and superconductivity in the telluride chalcogenides.