  We explore the influence of two different polarizations of quantum oxygen
vibrations on the spacial symmetry of the bound magnetic bipolaron in the
context of the t-J model by using exact diagonalization within a limited
functional space. Quadratic electron phonon coupling to transverse polarization
stabilizes d-wave symmetry. The existence of a magnetic background is essential
for the formation of a d-wave bipolaron state. With increasing linear electron
phonon coupling to longitudinal polarization the symmetry of a d-wave bipolaron
state changes to a p-wave. Bipolaron develops a large anisotropic effective
mass.
