The title compound, unimer U (tpy stands for 2,2′:6′,2″-terpyridin-4′-yl end-group), by itself shows the memristor effect with a retention time of 18 h and persistence of 11 h. Its coordination copolymer with Co(II) ions, [CoU]n, exhibits multimodal resistance changes similar to the synaptic responses observed in biological systems. More than 320 cycles of potentiation and depression measured in continuous sequence occurred without observing a significant current change, confirming the operational stability and reproducibility of the device based on the [CoU]n polymer. The synaptic effect of a device with an indium tin oxide (ITO)/[CoU]n/top-electrode (TE) configuration is more pronounced for the device with TE = Au compared to devices with TE = Al or Ga. However, the latter TEs provide a cost-effective approach without any significant compromise in device plasticity. The detected changes in the synaptic weight, about 12% for pair-pulse facilitation and 80% for its depression, together with a millisecond trigger and reading pulses that decay exponentially on the time scale typical of neurosynapses, justify the device’s ability to learn and memorize. These properties offer potential applications in neuromorphic computation and brain-inspired synaptic devices.