Vortex-Induced Vibrations (VIV) and Fluid-Structure Interaction (FSI) are critical engineering phenomena impacting the safety of structures ranging from offshore risers to long-span bridges. Predicting these vibrations is challenging because high-fidelity CFD simulations are often too computationally expensive. We address this limitation by presenting a data-driven Reduced Order Model (ROM) implemented in the ITHACA-FV open-source library. This approach combines physical accuracy with computational efficiency by constructing a low-dimensional subspace using Proper Orthogonal Decomposition (POD) and projecting the governing equations via Galerkin projection, building upon data-driven methods for turbulent flows [1]. To handle the moving mesh, we employ a data-driven Radial Basis Function (RBF) interpolation strategy that rapidly reconstructs the reduced operators at each deformed configuration while predicting eddy viscosity to bypass expensive online calculations. Furthermore, the fluid and structural domains are integrated via a robust strong coupling algorithm extending segregated solver approaches [2]. Here, the structural dynamics are solved using the Newmark time integration scheme to ensure kinematic compatibility and numerical stability. The resulting model achieves a computational speed-up of over 100 times, reducing the simulation time from 1 hour and 40 minutes for the Full Order Model to just 58 seconds for the online method. This demonstrates the framework's value for both rapid design and rigorous engineering analysis.