There are many other types of pearls that have been found by fishermen, and others. Sometimes these pearls are very round and beautiful. And, if this is the case, then they are usually very rare as well. So, there have most likely been many attempts to culture these rare pearls just like your Akoya Pearls. Two examples of these pearls are Melo Melo pearls and Abalone pearls.
Melo Melo pearls are very rare and sought after in the pearl jewelry market. They are generally very round and extremely large. One has been found to be almost the size of a golf ball. Though attempts have been made to nucleate the Melo Melo oyster, and culture these pearls, nobody has yet been successful. Therefore, all Melo Melo pearls are completely natural.
Abalone pearls are also very rare and sought after. Culturing methods have been found, but are much more difficult to really experiment with. The reason for this is that abalone oysters are hemophiliacs, and therefore will bleed to death if cultured the same way as Akoya or freshwater pearls . The abalone pearl is popular in Australia and the South Sea region, but has yet to hit the main stage in North America.