  Triangular lattice delafossite compounds built from magnetic lanthanide ions
are a topic of recent interest due to their frustrated magnetism and
realization of quantum disordered magnetic ground states. Here we report the
evolution of the structure and electronic ground states of RbCe$X_2$ compounds,
built from a triangular lattice of Ce$^{3+}$ ions, upon varying their anion
character ($X_2$= O$_2$, S$_2$, SeS, Se$_2$, TeSe, Te$_2$). This includes the
discovery of a new member of this series, RbCeO$_2$, that potentially realizes
a quantum disordered ground state analogous to NaYbO$_2$. Magnetization and
susceptibility measurements reveal that all compounds manifest mean-field
antiferromagnetic interactions and, with the exception of the oxide, possess
signatures of magnetic correlations onset below 1 K. The crystalline electric
field level scheme is explored via neutron scattering and \textit{ab initio}
calculations in order to model the intramultiplet splitting of the $J=5/2$
multiplet. In addition to the two excited doublets expected within the $J=5/2$
manifold, we observe one extra, local mode present across the sample series.
This added mode shifts downward in energy with increasing anion mass and
decreasing crystal field strength, suggesting a long-lived anomalous mode
endemic to anion motion about the Ce$^{3+}$ sites.
