Polycrystalline samples of Ln2CoGe4O12 (Ln = Gd, Tb, Dy, Ho or Er) and LnBCoGe4O12 (B = Sc or Lu) have been prepared and characterised by a combination of magnetometry, 155Gd Mössbauer spectroscopy and, in the case of Tb2CoGe4O12 and TbScCoGe4O12, neutron diffraction. The holmium- and erbium-containing compositions remain paramagnetic down to 2 K, those containing dysprosium behave as spin glasses and the terbium and gadolinium-containing compounds show long-range magnetic order with transition temperatures below 4 K in all cases. The data can be rationalized qualitatively in terms of the interplay between magnetic anisotropy and crystal field effects.