The size and composition dependence of the optical gap of colloidal alloyed quantum dots (QDs) of Zn(Te1-xSex) and Zn(Te1-xSx) were calculated by the finite-depth-well effective mass approximation method. QDs that exhibited red, green and blue emission were explored to develop cadmium-free II-VI chalcogenide-based QD-phosphors. We considered that highly monodisperse colloidal QDs with diameters of 3-6 nm are easy to synthesize and II-VI semiconductor QDs usually exhibit a Stokes shift ranging between 50 and 150 meV. We showed that Zn(Te1-xSex) QDs with 0.02≤x≤0.68, and 0≤x≤0.06, and 0.66≤x≤0.9 may be expected to exhibit green, and blue emission, respectively. Zn(Te1-xSx) QDs with 0.26≤x≤0.37, 0.01≤x≤0.2 and 0.45≤x≤0.61, 0≤x≤0.02, and 0.63≤x≤0.72, should give red, green and blue emission respectively. On the basis of our calculations, we showed that Zn(Te,Se) and Zn(Te,S) QDs are very promising cadmium-free II-VI chalcogenide semiconductor QD phosphors.