  We have investigated the magnetic and magnetocaloric properties of
antiferromagnetic Ising spin chain CoV$_{2}$O$_{6}$ by magnetization and heat
capacity measurements. Both monoclinic $\alpha$-CoV$_{2}$O$_{6}$ and triclinic
$\gamma$-CoV$_{2}$O$_{6}$ exhibit field-induced metamagnetic transition from
antiferromagnetic to ferromagnetic state via an intermediate ferrimagnetic
state with 1/3 magnetization plateau. Due to this field-induced metamagnetic
transition, these systems show large conventional as well as inverse
magnetocaloric effects. In $\alpha$-CoV$_{2}$O$_{6}$, we observe field-induced
complex magnetic phases and multiple magnetization plateaux at low temperature
when the field is applied along $c$ axis. Several critical temperatures and
fields have been identified from the temperature and field dependence of
magnetization, magnetic entropy change and heat capacity to construct the
$H$-$T$ phase diagram. As compared to $\alpha$-CoV$_{2}$O$_{6}$,
$\gamma$-CoV$_{2}$O$_{6}$ displays a relatively simple magnetic phase diagram.
Due to the large magnetic entropy change and adiabatic temperature change at
low or moderate applied magnetic field, $\gamma$-CoV$_{2}$O$_{6}$ may be
considered as a magnetic refrigerant in the low-temperature region.
