In the proton counterflow model of a pulsar magnetosphere that we have recently proposed, nonrelativistic protons are supplied from the magnetosphere to flow toward the pulsar surface and screen an electric field above the polar cap region. In this Letter, we show that the proton counterflow is also suitable for the bunching of pair plasma. The two-stream instability is easily excited and can produce bunches of pairs with a relevant length scale to emit coherent curvature radiation.