  A new implementation of the finite amplitude method (FAM) for the solution of
the relativistic quasiparticle random-phase approximation (RQRPA) is presented,
based on the relativistic Hartree-Bogoliubov (RHB) model for deformed nuclei.
The numerical accuracy and stability of the FAM -- RQRPA is tested in a
calculation of the monopole response of $^{22}$O. As an illustrative example,
the model is applied to a study of the evolution of monopole strength in the
chain of Sm isotopes, including the splitting of the giant monopole resonance
in axially deformed systems.
