This study explores the dynamic contact response of a viscoelastic functionally graded material (FGM)-coated half-plane under a rigid flat punch subjected to a time-harmonic vertical force. The elastic modulus and mass density of the FGM coating vary exponentially along the thickness direction. The FGM coating and the homogeneous half-plane possess viscoelastic properties, which are described by a linearly hysteretic damping model. By applying the asymptotic method and the Fourier integral transform technique, the contact problem is converted into a Cauchy singular integral equation. The effects of excitation frequency, gradient index, damping factor ratio, and punch width on the vertical impedance and dynamic contact stress are analyzed. The results indicate that adjusting the gradient index of the FGM coating can significantly affect the contact stress and vertical impedance.