Amorphous carbon-based memristors with transparent conductive electrodes can be programmed both optically and electronically. We demonstrate neuromorphic logic and memory functions using light-gated amorphous carbon (a-C) memristors with indium-free transparent electrodes. The devices consist of insulating tetrahedral a-C layers with Pt top contacts supported on conductive zinc tin oxide electrodes with intentionally-oxygenated a-C interfaces. Resistive switching occurs by electron trapping/de-trapping, allowing low power, self-rectifying operation. Broadband light pulses evoke paired-pulse facilitation, emulating photonic coincidence detection. Coincidence detection was also achieved using heterogeneous optoelectronic inputs demonstrating dendritic computation at the single memory cell level.