Polycrystalline samples in the solid solution ZrMnCoGeO (x = 0.0, 0.5, 1.0, 1.5 and 2.0) have been prepared using the ceramic method and characterised by a combination of magnetometry, X-ray diffraction and neutron diffraction. They all adopt the space group P4/nbm with a ∼ 9.60, c ∼ 4.82 Å and show long-range magnetic order with transition temperatures, T, in the range 2 ≤ T/K ≤ 10. The underlying magnetic structure is the same in each case but the ordered spins lie along [001] when x = 0.0 and in the (001) plane for all other compositions. In all cases the magnetically-ordered phase is a weak ferromagnet although the magnitude of the spontaneous magnetisation and the strength of the coercive field are composition-dependent. The magnetic structure can be rationalized by considering the strengths of the interactions along the distinct M-O-Ge-O-M superexchange pathways in the crystal and the observed magnetic structure is entirely consistent with the predictions of ab initio calculations.