Positron impact scattering cross-sections for pyridine and pyrimidine are reported here. Spherical complex optical potential formalism is used to calculate the positronium formation, elastic, total, and differential cross-sections. The ionization cross-sections calculated here are obtained employing the complex scattering potential-ionization contribution method. To account for the complex molecular structure of the target, an effective potential method is employed in our formalism for the first time. The contribution from rotational excitation is also included, which shows a reasonable comparison with the experimental data. The results obtained using the modified approach are encouraging and show very good agreement with the measurements. The differential cross-section for pyridine is reported for the first time.