  The quadrupole collective Hamiltonian, based on relativistic energy density
functionals, is extended to include a pairing collective coordinate. In
addition to quadrupole shape vibrations and rotations, the model describes
pairing vibrations and the coupling between shape and pairing degrees of
freedom. The parameters of the collective Hamiltonian are determined by
constrained self-consistent relativistic mean-field plus
Bardeen-Cooper-Schrieffer (RMF+BCS) calculations in the space of intrinsic
shape and pairing deformations. The effect of coupling between shape and
pairing degrees of freedom is analyzed in a study of low-energy spectra and
transition rates of four axially symmetric $N=92$ rare-earth isotones. When
compared to results obtained with the standard quadrupole collective
Hamiltonian, the inclusion of dynamical pairing increases the moment of
inertia, lowers the energies of excited $0^+$ states and reduces the
E0-transition strengths, in better agreement with data.
