The study of pion-nucleon scattering is crucial in understanding strong interactions and isospin-dependent dynamics in nuclear and particle physics. In this work, we construct inverse potentials for pion-nucleon scattering using a piecewise smooth Morse function as a reference, focusing on single-channel scattering in the \( S_{11} \) and \( S_{31} \) states. The phase equations for the \( l = 0 \) channel are solved using the fifth-order Runge-Kutta method, and the model parameters are optimized by minimizing the mean squared error (MSE) between the computed and experimental phase shifts. The constructed potentials reveal distinct interaction characteristics for different isospin states, highlighting variations in strength and range. This study provides a reliable framework for modeling pion-nucleon interactions, offering insights into resonance behavior and the role of isospin in hadronic scattering.