We constrain AvERA cosmologies in comparison with the flat Λ-cold dark matter (ΛCDM) model using cosmic chronometer (CC) data and the Pantheon+ sample of type Ia supernovae (SNe Ia). The analysis includes fits to both CC and SN datasets using the dynesty dynamic nested sampling algorithm. For the model comparison, we used the Bayesian model evidence and Anderson-Darling tests applied to the normalized residuals to assess consistency with a standard normal distribution. Best-fit parameters were derived within the redshift ranges z ≤ 2 for CCs and z ≤ 2.3 for SNe. For the baseline AvERA cosmology, we obtained best-fit values of the Hubble constant of H0 = 68.32−3.27+3.21 km s−1 Mpc−1 from the CC analysis and H0 = 71.99−1.03+1.05 km s−1 Mpc−1 from the SN analysis, each consistent within 1σ with the corresponding AvERA simulation value of H(z = 0). While both the CC and SN datasets yield higher Bayesian evidence for the flat ΛCDM model, they favor the AvERA cosmologies according to the Anderson-Darling test. We have identified signs of overfitting in each model, which suggests the possibility of overestimating the uncertainties in the Pantheon+ covariance matrix.