Here we propose a novel, fully automated framework for accelerated design of underwater acoustic coatings, targeting the reduction of acoustic signature of naval platforms under operational conditions, by coupling Bayesian Optimization (BO) with a 2-step Finite Element Model (FEM). The developed FEMs evaluate the acoustic performance of polyurethane (PU) coatings with embedded metamaterial features under the influence of varying depth of operation i.e., hydrostatic pressure-dependent acoustic attenuation. The frequency-dependent viscoelasticity, which has often been ignored in previous studies, is also considered in the FEMs to obtain a realistic evaluation of the absorption behavior of these coatings over a wide range of operational frequencies. The main contribution of the proposed optimization framework is its efficient utilization of the expensive FEM simulations through BO. The desired broadband and low-frequency attenuation is achieved under the varying operating depth by an optimal design of the void layers. Moreover, this framework enables the targeted design of underwater acoustic coatings by effective exploration of the 10-dimensional, vast and computationally expensive design space, leading to a significant reduction in the number of simulations required to run compared to conventional exhaustive search strategies.