Numerical methods for two dimensional shallow water equations dominated by convection and Coriolis forces, i.e., {finite volume methods and discontinuous Galerkin}methods, usually lack enough precision and structure preservation around stationary solutions. This problem is normally produced by excessive numerical dissipation and the absence of a numerical technique that allows to preserve stationary solutions. Nowadays it is an active area of research, see, for example, https://doi.org/10.1137/22M1515707 . In this work, we propose a new well-balanced numerical method for the two dimensional shallow water equations with Coriolis forces, building on the idea in (https://doi.org/10.1007/s10915-020-01149-5) where the well-balanced property is achieved by computing discrete local stationary solutions at each cell. A core ingredient of this technique is the approximation of the stationary solution, which requires a discrete space for which the kernel of the discrete PDE operator contains the equilibria of interest. To meet this requirement we employ the Global Flux quadrature (GFQ) approach (see https://doi.org/10.1016/j.jcp.2023.112673), that in this work is applied locally to approximate the stationary solutions in each cell. This formulation yields local and small non-linear systems of equations, one per cell, that must therefore be solved cell-wise; in our case, these problems are handled via residual minimization using a L-BFGS method.