I don't think countries and states is a very good model to use when thinking of Oceania, because even when we can see clear evidence of a form of political power extending over multiple islands, it usually looks very different than what we expect states to.

For example, take the well known Yapese Empire in Micronesia. Yap is a high island which, all else bring equal, gives the inhabitants a greater control of resources than an atoll. One part of Yap was even able to exert a tributary relationship over many of the Caroline Islands. But, this was not a matter of administrators and standing armies, rather the Caroline Islanders were compelled by custom, social distinction, and a fear of Yapese ritual power. So, the Caroline Islanders would carry things like shell ornaments and coconut fiber rope as tribute, but interestingly they would be given as a form of chiefly redistribution food. Many anthropologists have noted that this is a pretty good deal for them, as it alleviated the uncertainty of atoll life. The Yapese tribute recipients, in turn, could use the tribute they receive to enhance their status on the island. Now, don't take this as a typical island relation. Hawaii, for example, had a true state, Easter Island and Mangaia are two examples in which an island had an institution of paramount chief which was competed over by the different chiefdoms. Pohnpei had a system of perpetual political control centered on the major complex of Nan Madol. So there was an enormous diversity of different systems of social organization.

One problem is that the systems of political relations can be difficult to reconstruct because of the scale of devastation colonialism wrought. The same sort of demographic apocalypses that occurred on the Americas also occurred in the Pacific. And of course, the islands themselves were not unchanging environments. There isn't really a pattern that prevailed through time and space, but looking for sharply drawn borders is generally going to confuse and obscure more than reveal.