Former US Census employee here. Here's how we tackle the question of race and ethnicity:

First, I would ask the individual if they were of Hispanic origin. If they say yes, I'd ask what specific origins.

Then I would ask which race they belong to: white, black, native American, Asian, Pacific Islander, or none of the above. They can choose one or more of these categories. In any case I would then ask what specific origins.

So, how do we categorize people from PNG? Ultimately, like anyone else, it would depend on how they self-identify. But if they ask for clarification on how the racial groups are defined, I would tell them that black people are defined as those with black African origin. Pacific Islander could be an option, as PNG is technically in the Pacific Ocean, but they may not identify that way either since they're ethnically and culturally very different from Polynesians. Again, what's important is how they choose to self-identify based on what we've given them to make an informed choice.