© 2016 American Physical Society. 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 Hb is very similar to that of the parent compound Ni3V2O8 for the commonly involved phases, the zero-field phases in (Ni0.9Co0.1)3V2O8 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-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-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.