Frustrated lanthanide oxides are promising candidates for cryogen-free magnetic refrigeration due to their suppressed ordering temperatures and high magnetic moments. While much attention has been paid to the garnet and pyrochlore lattices, the magnetocaloric effect in frustrated face-centered cubic (fcc) lattices remains relatively unexplored. We previously showed that the frustrated fcc double perovskite Ba2GdSbO6 is a top-performing magnetocaloric material (per mol Gd) because of its small nearest-neighbor interaction between spins. Here we investigate different tuning parameters to maximize the magnetocaloric effect in the family of fcc lanthanide oxides, A2LnSbO6 (A = {Ba2+, Sr2+} and Ln = {Nd3+, Tb3+, Gd3+, Ho3+, Dy3+, Er3+}), including chemical pressure via the A site cation and the magnetic ground state via the lanthanide ion. Bulk magnetic measurements indicate a possible trend between magnetic short-range fluctuations and the field-temperature phase space of the magnetocaloric effect, determined by whether an ion is a Kramers or a non-Kramers ion. We report for the first time on the synthesis and magnetic characterization of the Ca2LnSbO6 series with tunable site disorder that can be used to control the deviations from Curie-Weiss behavior. Taken together, these results suggest fcc lanthanide oxides as tunable systems for magnetocaloric design.