We present macroscopic and neutron diffraction data on multiferroic lightly Co doped Ni3V2O8. The magnetic H-T phase diagrams have been derived from magnetization and electric polarization measurements with field directions parallel to the principal crystallographic axes. While the phase diagram for H parallel to b is very similar to that of the parent compound Ni3V2O8 for the commonly involved phases, the zero-field phases in (Ni0.9Co0.1)(3)V2O8 show a stronger instability for applied magnetic fields along the a or c axis. Neutron single-crystal diffraction revealed the magnetic structure of the field-induced phase for H parallel to c with a collinear spin alignment along the a and b axes for the two magnetically inequivalent sites. A pronounced irreversibility has been observed for the transition between the zero-field spin cycloid and the field-induced phase, which is manifested in a propagation vector change from q = (0.322 0 0) to q = (0.306 0 0), with slight modifications of the magnetic structure after reentering the zero-field phase. The reentrant phase is characterized by a significantly larger b component of the cross-tie site spin, therefore showing remanent features of the high-field phase. For H parallel to a the magnetization data reveal anomalies, one of which was proved to reflect a field-induced transition from the cycloidally to the sinusoidally modulated magnetic structure.