The superior piezoelectric (PE) performance of devices based on thin-films of wurtzite (w) w- alloys has motivated research efforts to determine the material properties of other alloys of aluminum nitride and rare-earth nitride (w-). The longitudinal PE, elastic and dielectric properties of substitutional w- alloys have been calculated with density-functional perturbation theory. The rare-earth elements in the simulations stand for scandium, yttrium and seven lanthanides: lanthanum, neodymium, gadolinium, dysprosium, erbium, ytterbium, and lutetium. The structure of the investigated alloys is modeled with special quasirandom supercells at rare-earth nitride fractions of 0.0625 and 0.25. The electrons of the lanthanides are incorporated in the pseudopotential core, an approach supported by the standard model of lanthanide chemistry. An increase of the PE stress coefficient and a softening of the stiffness coefficient are found for all investigated alloys for = 0.25, when compared to w-AlN. This leads to significant improvements of the PE strain effective coefficient of films of these alloys. For w-, the increases by compared to pure w-AlN. Increased displacement-response internal-strains and Born effective charges are demonstrated for all alloys at = 0.25, in a manner consistent with the behavior of w- alloys, suggesting shared intrinsic properties for the entire w- alloy family. Distortions of the alloy structure, correlated with the ionic radius of the rare earths, negatively affect their PE properties. At a small fraction = 0.0625, the alloys incorporating Sc, Y, Er, Yb, and Lu possess PE coupling coefficients greater than for w-AlN.