  We study by exact diagonalization the two-dimensional t-J-Holstein model near
quarter filling by retaining only few phonon modes in momentum space. This
truncation allows us to incorporate the full dynamics of the retained phonon
modes. The behavior of the kinetic energy, the charge structure factor and
other physical quantities, show the presence of a transition from a delocalized
phase to a localized phase at a finite value of the electron-phonon coupling.
We have also given some indications that the e-ph coupling leads in general to
a suppression of the pairing susceptibility at quarter filling.
