The Duffin-Kemmer-Petiau (DKP) equation is a relativistic wave equation governing the dynamics of spin-0 and spin-1 bosonic particles. In this work, we study the \((1+3)\) -dimensional DKP equation with a spatially dependent mass under a modified deformed exponential type potential. Using the framework of supersymmetric quantum mechanics, we derive approximate analytical solutions. A novel extension of the Pekeris approximation is introduced to treat the centrifugal barrier, enabling the complete determination of the energy spectrum. The non-relativistic limit of the DKP equation is obtained via an established transformation technique. The model is applied to diatomic molecules including lithium hydride (LiH), hydrogen chloride (HCl), \(^{7}\textrm{Li}_{2}\) , \(\textrm{Na}_{2}\) , and ScI. The energy spectra are computed for various quantum states \(\left| n,l,j\right\rangle \) using both relativistic and non-relativistic expressions. For LiH and HCl, where experimental data are scarce, our results show strong agreement with earlier theoretical predictions. For \(^{7}\textrm{Li}_{2}\) , \(\textrm{Na}_{2}\) , and ScI, the calculated energies align excellently with available experimental data. The proposed framework provides a reliable and analytically tractable tool for studying bosonic systems with position-dependent effective masses.
