  We study the effect of diagonal and off-diagonal electron-phonon coupling in
the ground state properties of the t-J model. Adiabatic and quantum phonons are
considered using Lanczos techniques. Charge tiles and stripe phases with mobile
holes (localized holes) are observed at intermediate (large) values of the
diagonal electron-phonon coupling. The stripes are stabilized by half-breathing
modes, while the tiles arise due to the development of extended breathing
modes. Off-diagonal terms destabilize the charge inhomogeneous structures with
mobile holes by renormalizing the diagonal coupling but do not produce new
phases. Buckling modes are also studied and they seem to induce a gradual phase
separation between hole rich and hole poor regions. The pairing correlations
are strongly suppressed when the holes are localized. However, in charge
inhomogeneous states with mobile holes no dramatic changes, compared with the
uniform state, are observed in the pairing correlations indicating that D-wave
pairing and moderate electron-phonon interactions can coexist.
