Crystal and magnetic structures of the $x=0.2$ member of La$_{rm 0.8-x}$Tb$_{rm x}$Ca$_{0.2}$CoO$_3$ perovskite series have been determined from the powder neutron diffraction. Enhancement of the diffraction peaks due to ferromagnetic or cluster glass ordering is observed below $T_C=55$ K. The moments evolve at first on Co sites, and ordering of Ising-type Tb$^{3+}$ moments is induced at lower temperatures by a molecular field due to Co ions. The final magnetic configuration is collinear F$_x$ for cobalt subsystem, while it is canted F$_x$C$_y$ for terbium ions. The rare-earth moments align along local Ising axes within textit{ab}-plane of the orthorhombic $Pbnm$ structure. The behavior in external fields up to $70-90$ kOe has been probed by the magnetization and heat capacity measurements. The dilute terbium ions contribute to significant coercivity and remanence that both steeply increase with decreasing temperature. A remarkable manifestation of the Tb$^{3+}$ Ising character is the observation of a low-temperature region of anomalously large linear term of heat capacity and its field dependence. Similar behaviours are detected also for other terbium dopings $x=0.1$ and 0.3.