These are species with at least one recorded territory in Fiji, 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 Fiji, among those a photograph exists for. Most recorded is not most numerous: it rewards animals that are common, conspicuous and live where people go.

Myiagra vanikorensis

Aerodramus spodiopygius

Myzomela jugularis

Todiramphus sacer

Ducula latrans

Lalage maculosa

Foulehaio procerior

Erythrura pealii

Artamus mentalis

Vini solitaria

Horornis ruficapilla

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