Within the framework of Feynman-Kleinert variational theory, simple equations for correlation functions of arbitrary nonlinear operators are derived. These correlation functions, meaningful only for short times, are extended to longer times by a well established ansatz. The approach is tested against exact results for the quantum force correlation function in a two-dimensional Helium cluster problem and is found to perform very well. The theory is also applied to calculate quantum force correlation functions for a diatomic in a larger Neon bath. The results indicate that the method is effective for vibrational energy relaxation processes in simple liquids when quantum effects are significant.