We investigated the phase stability, crystal structure, magnetism, specific heat, and resistivity of $R{\mathrm{Co}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ $(R=\mathrm{La},$ Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Y, Er). $R{\mathrm{Co}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ crystallizes in the ${\mathrm{LuNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$-type structure and the evolution of their unit-cell metric properties with the R size is governed by the lanthanide contraction: a faithful replica, though with a shrinking unit cell, of the behavior observed in the isomorphous $R{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ series. In spite of such structural similarity, their magnetic and superconducting features are distinctly different. For all the studied $R{\mathrm{Co}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ and down to 30 mK, no superconductivity was detected though their Sommerfeld constants $\ensuremath{\gamma}$ are comparable to those of the superconducting $R{\mathrm{Ni}}_{2}{\mathrm{B}}_{2}\mathrm{C}.$ ${T}_{N}$ of all $({\mathrm{PrCo}}_{2}{\mathrm{B}}_{2}\mathrm{C},$ due to hybridization, is an exception) are systematically lower than their Ni-based isomorphs and, furthermore, do not obey the de Gennes scaling. Such a breakdown, confirmed also in $({\mathrm{Dy}}_{1\ensuremath{-}x}{\mathrm{Gd}}_{x}){\mathrm{Co}}_{2}{\mathrm{B}}_{2}\mathrm{C},$ is attributed to crystal field effects on the R ions (Co ions are nonmagnetic). Below ${T}_{N},$ a zero-field order-to-order phase transition was observed in $R=\mathrm{Nd},$ Sm, Tb, Dy, Ho, Er but not in the spherical $R=\mathrm{Gd};$ emphasizing the role of the magnetic anisotropy. Finally, the character and dimensionality of the low-temperature spin waves are discussed.