Coatings widely applied on the surfaces of tribological components often exhibit depth-dependent material properties, and their optimal design requires the thorough understanding of contact mechanics for functionally graded (FG) coatings. However, most existing studies have adopted the assumption of an infinite-width coating, which differs significantly from the selective coating strategies commonly employed in engineering applications. Therefore, this paper develops a semi-analytical contact model for finite-width FG coatings. The coating modulus is allowed to vary arbitrarily along the depth direction, and no strict limitations are imposed on the coating width. The void zones flanking the coating are treated as zero-modulus coating segments, thereby extending the original coating into a fictitious infinitely wide layer. The modulus difference between coating and substrate enables the inclusion description of the coating, and the resulting disturbances are explicitly quantified through eigenstrains and related analytical solutions. In combination with the coupled relationship between the normal traction and the eigenstrain, the conjugate gradient (CG) method is used to robustly solve for the required normal traction. Parametric investigations based on the developed model demonstrate that increasing the coating modulus elevates structural stiffness and enhances contact stresses; the decreased distance from one coating edge to the initial contact point increases the normal traction and causes its profile to shift away from that edge, but the two edge effects vanish when the distance exceeds a certain threshold; deepening the FG coating intensifies the edge effects and amplifies the influence of the elastic dissimilarity between the coating and the substrate.