Yes, there is gold in Little Oyster Cove rivulet (NOT Oyster Cove Rivulet), but you have to be near the outcrops of syenite porphyry that are up in the hills. I used to live in Woodbridge and had a couple of friends with properties in the area, so I did some investigating.
There were never significant workings in this area, it is only noteworthy as an occurrence. The occurrences are all inside private property. I once found a tiny speck behind the church near sea level, but I had to do a ton of work for a bit you couldn’t even see without a magnifying glass. Near the outcrops you can get occasional flyspeck sized bits.
The Cygnet/Lymington occurrences that are tied to the same geological event were way more productive, and have had active workings in the early 20th century. They are mostly inside private property also, except for a short stretch of Forsters Rivulet in Lymington, and some foreshore occurrences in the Petcheys Bay and Wheatleys Bay areas.