Naturalisation records are held by the National Archives of Australia. Records for the Province of South Australia before 1904 are available at their Adelaide Office.
Information that may be found includes:
The National Archives of Australia has recently published Commonwealth Government records about South Australia and a version is available online. Chapter 10 outlines information pertaining to naturalisation that is worth exploring.
The State Library holds various indexes and records pertaining to naturalisation. To learn more click on the link below.
The National Archives of Australia has digitised many of its historical records, including naturalisation records, and these are now available online.