Bayesian inference is employed to precisely evaluate single crystal elastic properties of novel γ- γ′ Co- and CoNi-based superalloys from simple and non-destructive resonant ultrasound spectroscopy (RUS) measurements. Nine alloys from three Co-, CoNi-, and Ni-based alloy classes were evaluated in the fully aged condition, with one alloy per class also evaluated in the solution heat-treated condition. Comparisons are made between the elastic properties of the three alloy classes and among the alloys of a single class, with the following trends observed. A monotonic rise in the c44 (shear) elastic constant by a total of 12 pct is observed between the three alloy classes as Co is substituted for Ni. Elastic anisotropy (A) is also increased, with a large majority of the nearly 13 pct increase occurring after Co becomes the dominant constituent. Together the five CoNi alloys, with Co:Ni ratios from 1:1 to 1.5:1, exhibited remarkably similar properties with an average A 1.8 pct greater than the Ni-based alloy CMSX-4. Custom code demonstrating a substantial advance over previously reported methods for RUS inversion is also reported here for the first time. CmdStan-RUS is built upon the open-source probabilistic programing language of Stan and formulates the inverse problem using Bayesian methods. Bayesian posterior distributions are efficiently computed with Hamiltonian Monte Carlo (HMC), while initial parameterization is randomly generated from weakly informative prior distributions. Remarkably robust convergence behavior is demonstrated across multiple independent HMC chains in spite of initial parameterization often very far from actual parameter values. Experimental procedures are substantially simplified by allowing any arbitrary misorientation between the specimen and crystal axes, as elastic properties and misorientation are estimated simultaneously.