To sleet? it's happened a lot I think, rain almost never. I guess it also depends what you define near the coast, for example March 2017 in lower Westchester was snow to sleet to snow with almost a foot of snow and lots of sleet.
Honestly now that i think of it it's happened many times even in the city I just can't remember exact dates, snowicane was another example that comes to mind with 12+ despite different precip types. There was another storm I believe that same winter that was snow to sleet/drizzle to snow that dumped like 19 inches in Queens.