  Single crystals of RCo$_{2}$Ge$_{2}$ (R = Y, La-Nd, Sm-Tm) were grown using a
self-flux method and were characterized by room-temperature powder x-ray
diffraction; anisotropic, temperature and field dependent magnetization;
temperature and field dependent, in-plane resistivity; and specific heat
measurements. In this series, the majority of the moment-bearing members order
antiferromagnetically; YCo$_{2}$Ge$_{2}$ and LaCo$_{2}$Ge$_{2}$ are
non-moment-bearing. Ce is trivalent in CeCo$_{2}$Ge$_{2}$ at high temperatures,
and exhibits an enhanced electronic specific heat coefficient due to Kondo
effect at low temperatures. In addition, CeCo$_{2}$Ge$_{2}$ shows two
low-temperature anomalies in temperature-dependent magnetization and specific
heat measurements. Three members (R = Tb-Ho) have multiple phase transitions
above 1.8 K. Eu appears to be divalent with total angular momentum L = 0. Both
EuCo$_{2}$Ge$_{2}$ and GdCo$_{2}$Ge$_{2}$ manifest essentially isotropic
paramagnetic properties consistent with J = S = 7/2. Clear magnetic anisotropy
for rare-earth members with finite L was observed, with ErCo$_{2}$Ge$_{2}$ and
TmCo$_{2}$Ge$_{2}$ manifesting planar anisotropy and the rest members
manifesting axial anisotropy. The experimentally estimated crystal electric
field (CEF) parameters B$_{2}^{0}$ were calculated from the anisotropic
paramagnetic $\theta_{ab}$ and $\theta_{c}$ values and follow a trend that
agrees well with theoretical predictions. The ordering temperatures, T$_{N}$,
as well as the polycrystalline averaged paramagnetic Curie-Weiss temperature,
$\Theta_{avg}$, for the heavy rare-earth members deviate from the de Gennes
scaling, as the magnitude of both are the highest for Tb, which is sometimes
seen for extremely axial systems. Except for SmCo$_{2}$Ge$_{2}$, metamagnetic
transitions were observed at 1.8 K for all members that ordered
antiferromagnetically.
