Molybdenum diboride is unique among transition metal diborides because it exists in both hexagonal (AlB2-type) and rhombohedral structures. However, it is difficult to stabilize the superconducting AlB2-type phase, which requires either extreme synthesis condition or suitable chemical doping. Here we report the structural and physical properties of Sc-doped nonstoichiometric molybdenum diborides (Mo0.95Sc0.05)1-xB2 and (Mo1-yScy)0.71B2 prepared by the common arc melting method. The AlB2-type phase is found to form over wide ranges of 0 ≤ x ≤ 0.29 and 0.025 ≤ y ≤ 0.30 for the first time, and bulk superconductivity with Tc up to 7.9 K is observed. Tc increases with increasing x in the (Mo0.95Sc0.05)1-xB2 series, but evolves nonmonotonically with varying y in the (Mo1-yScy)0.71B2 series. Despite this contrast, Tc of both borides follows nearly the same linear dependence on the electron-phonon coupling constant, suggesting that it is mainly controlled by the electron-phonon interaction. In addition, the stabilization of AlB2-type structure is attributed to the decrease in the number of d electrons as a consequence of Sc doping, which suggests that a similar effect may be achieved by substituting Mo with other d electron-poorer metal elements.