I found these two discs on the same island, but 18 months apart from one another. They are both genuine coral of the same species. At first I thought that they might be bone, but a friend of mine who dives confirm that they are pieces of coral that have been worn away like sea glass.
The larger one is 1 1/8 inch by 3/4 inch. The smaller one is 7/8 inch by 3/4 inch. The thickness varies from 1/8 inch to 1/4 inch.
They would be lovely on a natural yarn hand-knit or hand-crocheted sweater. They look pretty nice against un-dyed linen as well.