We have earlier proposed a fourth order gravity model as a possible explanation for late time cosmic acceleration and for flattened galaxy rotation curves. The model has a free length parameter whose value depends on the scale of the system under study (e.g., the whole Universe, a galaxy, or a compact binary pulsar). In the present work, we investigate the constraints imposed on the free model parameter by PSR (Hulse-Taylor binary pulsar), PSR , and PSR J0737-3039 data: periastron advance, and emission of gravitational waves and consequent period decay. It is shown that the model is consistent with these observations, provided the length parameter is bounded from above, but is unstable due to the presence of ghost degrees of freedom.