  Effects of a single-ion anisotropy on magnetocaloric properties of selected
spin-$s\geq 1$ antiferromagnetic Ising clusters with frustration-inducing
triangular geometry are studied by exact enumeration. It is found that
inclusion of the single-ion anisotropy parameter $D$ can result in a much more
complex ground-state behavior, which is also reflected in a magnetocaloric
effect (MCE) at finite temperatures. For negative $D$ (easy-plane anisotropy)
with increasing $s$ the ground-state magnetization as a function of the
external field gradually shows increasing number of plateaus of various
heights. Except for the cases of integer $s$ with $D < D_0 \leq 0$, the first
magnetization plateau is of non-zero height. This property facilitates an
enhanced MCE in the adiabatic demagnetization process in the form of an abrupt
decrease in temperature as the magnetic field vanishes to zero. The cooling
rate can be considerably enhanced in the systems with larger $s$ and $D>0$
(easy-axis anisotropy), albeit its dependence on these parameters is strongly
dependent on the cluster geometry. From the studied systems more favorable
conditions for observing a giant MCE were found in the 2CS cluster, consisting
of two corner-sharing tetrahedra, the experimental realization of which could
be technologically used for efficient refrigeration to ultra-low temperatures.
