Two pyridinecarboxamide cobalt dicyanide building blocks and Mn(III) compounds have been employed to assemble cyanide-bridged heterometallic complexes, resulting in three trinuclear cyanide-bridged $Co^{III}-Mn^{II}$ complexes: ${[Mn(MeOH)_4][Co(bpb)(CN)_2]_2}{cdot}2MeOH{cdot}2H_2O$ (1), ${[Mn(MeOH)_4][Co(bpmb)(CN)_2]_2}{cdot}2MeOH{cdot}2H_2O$ (2) and ${[Mn(DMF)_2(en)_2][Co(bpb)(CN)_2]_2}{cdot}2DMF{cdot}H_2O$ (3) ($bpb^{2-}$ = 1,2-bis(pyridine-2-carboxamido)benzenate, $bpmb^{2-}$ = 1,2-bis(pyridine-2-carboxamido)-4-methyl-benzenate, en = ethylenediamine). Single crystal X-ray diffraction analysis shows their similar sandwich-like structures, in which the two cyanide-containing building blocks act as monodentate ligands through one of their two cyanide groups to coordinate the Mn(II) center. For complex 3, it was further linked into one-dimensional structure by ethylenediamine acting as bridges. Investigation of the magnetic properties of complex 3 reveals weak antiferromagnetic coupling between the neighboring Mn(II) centers through the bridging ethylenediamine molecule. A best-fit to the magnetic susceptibilities of complex 3 gave the magnetic coupling constant J = -0.073(2) $cm^{-1}$.