Our working hypothesis is that this is an oncolite.
These can be deposited by algae, and would be consistent with the area where you have found them.
There was a large paleo-lake, Lake Manuherikia, in the area, and these may have been deposited in the shoreline waters of the old lake.
The excerpt below is from an report noting:
‘Ostracods, algae (including oncolites), fish and bird remains are dispersed within shoreline facies.’
Lignite Resources of Central Otago by B.J. Douglas 1986 pg ii
I think the best sedimentary indications of the lake are at Bannockburn but the fossil remains are not really very spectacular though one day someone will find something there and reptilian remains etc have already been found in the form of crocodile bone and tooth.
A lot of diverse fossils including extinct bird, fish and small seeds from trees etc.
What are the first 2 pics of ?
Lake Manuherikia is a very fascinating subject in its entirety & a very complex geological event that today you would be very hard pressed to know that is ever existed when driving through Central Otago.
Here are a couple of links you may find interesting.
JW 
Agree the Aronui channel (Late Pleistocene) and Fruitlands Flat channel (middle Pleistocene).
The little object was found at the mid creek section on Butcher creek, on top of the Miocene sediments.
What is the “little object” ?
That’s my guest…
If those little Ooids poohed gold then I’m all ears.
What do you recon…need a ladder 8m
Its not pidgen remains, white quartz. What do you think…
Cant reach need a drone
regards
Glen Callanan
Doesn’t look like quartz. By pigeon remains are you meaning pigeon poo? Of which it quite possibly could be.
JW 
I found two of these some years ago while panning of all things. They are quite light and look for all the world like little flattened button mushrooms. Always wondered what they were! About 15 to 20mm across.
