Molecular-level simulation can effectively complement continuum analysis for the study on the damping mechanisms of acoustic vibrations of nanostructures in aqueous environment, which is central to the applications of nanostructures in high-sensitivity sensing and detection. It is highly desirable to develop coarse-grained (CG) water models that can accurately reproduce the density, compressibility, and viscosity of water simultaneously, for the molecular simulations of vibrations of nanostructures in water at affordable computational cost. In this work, the CG water models based on Lennard-Jones potential have been developed with each CG particle representing three and four water molecules. The deep neural networks have been trained using the data generated by CG molecular-dynamics simulations and used to solve the inverse problem of parameterization of the CG force fields for the target properties of water. As compared with many other existing CG models, the proposed CG water models are advantageous in terms of the ability to accurately predict the experimentally measured density, compressibility, and viscosity of water simultaneously, which is essentially important for the faithful molecular-level descriptions of the damping effect of the surrounding water on mechanical vibrations of nanostructures. Further comparisons suggest that the proposed three-to-one CG water model is a preferable option for molecular simulations of vibrations of nanostructures in water, due to its more accurate descriptions of target water properties.