Atomic force microscopy (AFM) has evolved into a powerful instrument for examining material properties at the nanoscale. However, quantifying viscoelasticity using AFM remains a challenging task, since existing methods face sensitivity issues when it comes to the separation of viscous and elastic material properties. Here, a method is proposed that utilizes the nonlinear dynamic response of the AFM cantilever to effectively disentangle and independently quantify the dissipative and conservative parts of the tip-sample interaction force. Through measurements on one and two component solvent-borne coatings, it is demonstrated that the strength of the nonlinearity of AFM cantilever motion is predominantly determined by the elasticity of the sample, whereas the detuned frequency of the nonlinear resonance is contingent on the viscosity. The sensitivity of the quantified values is discussed by comparing the results to those of established multi-frequency AFM measurements, showing good agreement. These findings underscore the effectiveness of nonlinear dynamic AFM for deciphering viscous and elastic material properties, potentially accelerating the development cycles of polymeric coating materials.