Double-perovskite iridates A2ZnIrO6 (A=alkaline or lanthanide) show complex magnetic behaviors ranging from weak ferromagnetism to successive antiferromagnetic transitions. Here we report the static (dc) and dynamic (ac) magnetic susceptibility and neutron powder diffraction measurements for A=La and Nd compounds to elucidate the magnetic ground state. Below 10 K, the A=La compound is best described as canted iridium moments in an antiferromagnet arrangement with a propagation vector k = 0 and a net ferromagnetic component along the c axis. On the other hand, Nd2ZnIrO6 is described well as an antiferromagnet with a propagation vector k = (1/2 1/2 0 ) below TN∼ 17 K. Scattering from both the Nd and Ir magnetic sublattices was required to describe the data, and both were found to lie almost completely within the ab plane. The dc susceptibility revealed a bifurcation between the zero-field-cooled and field-cooled curves below ∼13 K in Nd2ZnIrO6 . A glassy state was ruled out by ac susceptibility but detailed magnetic isotherms revealed the opening of the loop below 13 K. These results suggest a delicate balance exists between the Dzyaloshinskii-Moriya, crystal field schemes, and d-f interaction in this series of compounds.