Shallow water magnetohydrodynamics (SWMHD) is a recently proposed model for a thin layer of incompressible, electrically conducting fluid. The velocity and magnetic field are taken to be nearly two dimensional, with approximate magnetohydrostatic balance in the perpendicular direction, leading to a reduced two-dimensional model. The SWMHD equations have been found previously to admit unphysical cusp-like singularities in finite amplitude magnetogravity waves. This paper extends the Hamiltonian formulation of SWMHD to construct a dispersively regularized system, analogous to the Green–Naghdi equations of hydrodynamics, that supports smooth solitary waves and cnoidal wave trains, and shares the potential vorticity conservation properties of SWMHD.