This research introduces a novel approach to calculating the binary distribution function of the one-component plasma (OCP) model using the Bilal distribution. The OCP, a fundamental model in plasma physics, is essential for understanding phenomena in fields such as astrophysics, condensed matter physics, and inertial confinement fusion. By employing the Bilal distribution, which offers superior flexibility in fitting non-standard data, we aim to provide a more accurate representation of the pair correlation function in the OCP. Our findings reveal that the Bilal distribution yields result that are in excellent agreement with Monte Carlo simulations and other theoretical predictions. The enhanced flexibility of the Bilal distribution allows for a more accurate description of the short-range and long-range correlations between particles, which are crucial for understanding the thermodynamic properties of the OCP. Additionally, we have investigated the effects of various system parameters, such as the coupling parameter, on the binary distribution function.