  We investigate the nature of the ground state of the one-dimensional t-J
model coupled to adiabatic phonons by use of the Lanczos technique at quarter
filling. Due to the interplay between electron-electron and electron-phonon
interactions, the model undergoes instabilities toward the formation of lattice
and charge modulations. Moderate on-site and intra-site electron-phonon
couplings lead to a competition of different spin-Peierls and dimerized states.
In the former case two electrons belong to the unit cell and we expect a
paramagnetic band insulator state, while lattice dimerization leads to a Mott
insulating state with quasi long range antiferromagnetic order. The zero
temperature phase diagram is obtained as a function of intra-site and
inter-site electron-phonon couplings, analytically in the $J\to 0$ limit and
numerically at finite J/t.
