Turbulent flows on planets and stars organize themselves into striking banded patterns and jets, yet the mechanism that generates these large scale structures is not well understood using classical linear instability theory. Using statistical state dynamics (SSD) theory, self organization of these jets is understood to arise from interaction between the jet and its associated turbulent Reynolds stresses, which is a nonlinear interaction. While SSD theory for hydrodynamics of coherent structure interaction with turbulence has provided us understanding of jet formation and maintenance explaining many of the observations of jets in the atmospheres of Earth, Jupiter, and other planets, this understanding is not comprehensive because the magnetized nature of some planetary and stellar atmospheres and interiors necessitates an extension to magnetohydrodynamics. In this work, we extend SSD theory to study large scale structure formation in shallow-water magnetohydrodynamic turbulence on an equatorial beta-plane. The analysis reveal formation and equilibration of zonal jet-toroidal field structure (ZJTFS) with both fixed point and time-dependent behavior with implications for the 22 year solar cycle.