Fiji and Auckland are typically on the same time or within 1 hour of each other. Both use UTC+12, but their daylight saving schedules differ. Fiji uses Fiji Time (FJT, UTC+12/+13) and Auckland uses New Zealand Standard/Daylight Time (NZST/NZDT, UTC+12/+13).
During periods when only one observes daylight saving, there may be a 1-hour difference.
Any time works most of the year! Since both locations are usually synchronized or close, you can schedule calls during standard business hours (9:00 AM - 6:00 PM) without significant adjustment.
Fiji and Auckland have strong connections through tourism and trade. Auckland is a major hub for flights to and from Fiji. Many New Zealanders vacation in Fiji, and there are significant business and cultural ties between the two.