  The orthoperovskites TbCoO$_3$ and DyCoO$_3$ with Co$^{3+}$ in a non-magnetic
low-spin state have been investigated by neutron diffraction down to 0.25 K.
Magnetic ordering is evidenced below $T_N=3.3$ K and 3.6 K, respectively, and
the ordered arrangements are of canted type, A$_x$G$_y$ for TbCoO$_3$ and
G$_x$A$_y$ for DyCoO$_3$ in Bertaut's notation. The experiments are confronted
with the first-principle calculations of the crystal field and magnetism of
Tb$^{3+}$ and Dy$^{3+}$ ions, located in the $Pbnm$ structure on sites of $C_s$
point symmetry. Both these ions exhibit an Ising behavior, which originates in
the lowest energy levels, in particular in accidental doublet of non-Kramers
Tb$^{3+}$ ($4f^8$ configuration) and in ground Kramers doublet of Dy$^{3+}$
($4f^9$) and it is the actual reason for the non-collinear AFM structures. Very
good agreement between the experiment and theory is found. For comparison,
calculations of the crystal field and magnetism for other systems with Kramers
ions, NdCoO$_3$ and SmCoO$_3$, are also included.
