The detection of light at ultraviolet (UV) wavelengths is important for many military, medical and environmental applications. Applications such as biological agent detection and non-line-of-sight communications require the detection of scattered UV light. Currently, photomultiplier tubes operated as single photon counters are used to detect these low light levels, but they have many unfavorable characteristics for such applications. SiC based avalanche photodiodes (APDs) operated in Geiger mode could potentially meet the needs of these applications. Our first results, using SiC Geiger mode single photon counting avalanche photodiodes (SPADs), showed prohibitively high dark counts, due to a large tunneling current component in the multiplied dark current. Here we show the results of two p-i-n structures with 260µm and 480µm i-regions, which reduced the primary dark current by two orders of magnitude, operated under gated quenching conditions at 325nm. The lower dark current resulted in a dark count rate of 28kHz at 3.6% single photon detection efficiency (SPDE) in a 100µm diameter device. This is a three order reduction in the dark count rate over our previous results using a p-n junction SPAD.