Short answer: No.

As to why that is- it depends. Were you thinking pre-European arrival (pre-1800 lets say), European expansion/empire (1800-1960), or more modern era of decolonisation/post-colonial 1960-1995?

Generally speaking lets just say; pre-European arrival material gain wasn't measured by the same means as Europe (Venice, Genoa, Ragusa, etc), so there was no large scale established merchant empire in the same vein as what we see in Europe- nor any of that banking/financing infrastructure necessary- but then, wealth was measured very differently- if we can even say 'wealth' as a concept was measurable or measured by peoples in Oceania in any way compatible to pre-modern European or modern definitions.

Generally- after European expansion and colonization/empire, Oceania was a colony and therefor not the center of any merchant style republic.

Today- well, there have been some attempts at setting up something similar- perhaps most infamously by the shadowy Phoenix Institute (who are so much like a James Bond villain its absurd). This group attempted to build an artificial island not too far off Tonga, which was unsuccessful after the Tongan Kingdom sent ships over to claim the dredged island and enforce their territorial rights over the reefs and shoals on which the Phoenix Institute had believed it could establish a sort of libertarian republic. They did not give up and attempted to help fund a coup in the Bahamas to do the same thing and after that failed also attempted to do the same thing in Vanuatu after the British and French left the country. In no instance were they successful- but not for lack of trying!

David Robie's "Blood on their Banner" has some good sections on the Phoenix Institute though his main topic is the chaotic decolonization of France and Britain in Vanuatu.