A fully nonlinear treatment for stationary waves in a cold plasma with an ion beam propagating parallel to the magnetic field is carried out in the framework of Hall MHD. It is shown that the linearly unstable system can evolve into a steady nonlinear configuration in which both ion populations undergo a coherent helical motion guided by the magnetic field. The complete system of equations can be reduced to two coupled differential equations for the transverse proton (or beam ion) speed and the phase difference between the wave motion of both ion fluids. In the case of a weak beam these equations possess a phase-portrait integral which describes the main dynamical features of the system. A soliton-type solution with a core filled by smaller-scale oscillations is found for the transverse components of the ion velocities and magnetic field. It is suggested that gyrophased bunched ion beams associated with large-amplitude quasi-monochromatic ULF waves often observed in the ion foreshock are a manifestation of these fully nonlinear structures. A driver for such oscilliton-like structures is provided by a linear instability in which the wave is exponentially growing. The momentum exchange between two different ion populations, mediated by the magnetic field stresses, leads to the formation of a steady nonlinear wave-oscilliton.