There were a CJ Lindberg and a ? Lindberg both living in Ba in 1873. ? Lindberg would have been male, as females were not included in this list- The Fijian Almanac and Directory 1873.
In 1874 there were Chas J Lindberg and James Lindberg both living in Ba-Turpin's Fijian Nautical and Commercial Almanac and Fiji Directory- 1874.
In the 1874/75 Census of Europeans in Fiji neither of them is included.
In the 1879 Fiji Planting and Commercial Directory CJ Linberg is listed at Ba.
Fiji BDMs date from 1874, so if you can access them on Mormon microfilm you may find something. The Fiji Times newspaper, which began in 1869, has also been microfilmed, but you really need to have some dates before you start looking at a newspaper microfilm.
If you are in NZ, the Fiji BDMs are held at Auckland City Library Research Centre, but can be ordered to other Mormon Family Histoery Centres using the Familysearch website. This can be done in other countries too.
The Fiji Times microfilm are held at the National Library Wellington, and the Massey University Library, Albany, Auckland. There are copies in Australia as well.
Try looking at Trove and Papers Past. A lot of Fiji news was published in both Australia and NZ newspapers.