Four rare-earth cobalt arsenides, $RCo_{2}As_{2}$ (R = La, Ce, Pr, Nd), were obtained by reactions of constituent elements in molten Bi. The use of Bi flux also allowed the growth of representative single crystals. All compounds are isostructural and belong to the $ThCr_{2}Si_{2}$ type (space group I4/mmm). The formation of Co vacancies is observed in all structures, while the structures of La- and Ce-containing compounds also show incorporation of minor Bi defects next to the R crystallographic site. Correspondingly, the general formula of these materials can be written as $R_{1–x}Bi_{x}Co_{2−δ}As_{2}$, with $x/δ$ = 0.03/0.1, 0.05/0.15, 0/0.2, and 0/0.3 for R = La, Ce, Pr, and Nd, respectively. All compounds exhibit high-temperature ferromagnetic ordering of Co magnetic moments in the range 60–200 K. Electronic band structure calculations revealed a high peak in the density of states at the Fermi level, thus supporting the itinerant nature of magnetism in the Co sublattice. The magnetic ordering in the lanthanide sublattice takes place at lower temperatures, with the R moments aligning antiparallel to the Co moments to give a ferrimagnetic ground state. The measurements on oriented single crystals demonstrated significant magnetic anisotropy in the ferrimagnetic state, with the preferred moment alignment along the $\mathit{c}$ axis of the tetragonal lattice. Neutron powder diffraction failed to reveal the structure of magnetically ordered states but confirmed the presence of Co vacancies. X-ray absorption near-edge structure spectroscopy on $Ce_{1.95}Bi_{0.05}Co_{1.85}As_{2}$ showed the average oxidation state of Ce to be +3.06. Solid state NMR spectroscopy revealed a substantially reduced hyperfine field on the Co atoms in the vicinity of Bi defects.