Granular bed motion induced by a liquid shear flow is considered as a model of bedload. This flow is characterized by a localization of the granular flow close to the upper surface of the bed. In such a framework, the paper aims at discussing and proposing continuum effective models describing the physical properties, as the rheology, of the two-phase granular suspension at a so-called mesoscale larger than the grain size. The main questions addressed here concern the relevance and the extension of effective rheological models for granular suspensions often extracted from simple-shear flow configurations in a viscous limit, to situations of both granular shear localization as in bedload and weakly inertial flow regime. For this purpose, we consider the steady transport of a granular bed by a laminar Couette fluid flow above it and close to the onset of motion, for a grain-to-fluid density ratio of 2.5, as silica in water, and a range of particle Reynolds numbers Rep ∈ [0.1, 10] and Shields numbers θ ∈ [0.1, 0.7]. To provide accurate continuum models, the dynamics into the granular shear layer has to be first known down to a scale smaller than each grain, a so-called microscale. Numerical simulations are thus performed at the microscale at which individual grain dynamics is resolved, using an immersed boundary method (IBM) coupled to a discrete element method (DEM) granular solver. Upscaling is then performed to obtain the equivalent momentum balance at the mesoscale, characterized by continuum phases, using a spatial averaging method on volume element larger than the grain diameter. This approach allows us obtaining stresses, strains, and their relationships for the fluid phase, the granular phase, and the equivalent mixture, independently. The main contribution of this work is threefold: (i) we highlight the relevance of mesoscopic rheological continuum law for localized granular shear flow; (ii) we extract rheological models from direct numerical simulations (IBM/DEM) in a weakly inertial regime, going beyond purely viscous situations; and (iii) we extend Coulomb-like model μ(I ) of a granular suspension to incorporate fluid/particle inertial effects showing a different dependence of fluid phase and granular phase contributions with dimensionless numbers.