Ion acceleration in electrostatic collisionless shocks is driven by the interaction of the high-power laser with specially tailored near-relativistic critical density plasma. 2D EPOCH particle-in-cell simulations show that the ion acceleration is dependent on the target material used. In materials with low charge-to-mass ratio < Z/A >, proton beams with high flux and low energy spread are generated. In multi-ion plasmas the ions with different < Z/A > acquire different velocities under a non-oscillating component of electrostatic field in the upstream region. This relative drift between the protons (< Z/A > = 1) and the lower < Z/A > ions leads to the excitation of electrostatic ion two-stream instability. This in turn generates a low-velocity component in the upstream expanding protons. The velocity distribution of the upstream expanding protons is further broadened toward the higher velocity by the electrostatic ion two-stream instability between reflected protons, which results in large number of protons being accelerated by the shock.