These are species with at least one recorded territory in Papua New Guinea, not a national checklist: a bird list from eBird or Avibase is more complete. The counts follow recording effort as much as wildlife, so a country with more visitors and more naturalists will show more of both.
The species with the most open occurrence records in Papua New Guinea, among those a photograph exists for. Most recorded is not most numerous: it rewards animals that are common, conspicuous and live where people go.

Philemon buceroides

Collocalia esculenta

Eclectus roratus

Dicaeum geelvinkianum

Macropygia amboinensis

Trichoglossus haematodus

Rhipidura albolimbata

Melipotes fumigatus

Geoffroyus geoffroyi

Melidectes belfordi

Mino dumontii

Rhyticeros plicatus
The reference database has no regions filed under Papua New Guinea.
The field guide covers Papua New Guinea on the map, but none of its species have an entry written for them yet.