DCC parks and recreation group manager Robert West said the work would involve some "minor" excavation of part of the William Martin Reserve, which would then be back-filled with new material.
The area would then be compacted, and new topsoil added, to "blend" the work site into the surrounding area, he said.
The work was expected to cost about $10,000 and the council would "closely monitor the area for any further signs of subsidence", he said.
The plan came after the reserve was closed to the public on November 1, following the discovery of three small sinkholes above what was known to be the location of an abandoned underground coal mine.
A report by geotechnical engineering consultant GeoSolve, commissioned by the DCC, said the holes could be the first signs of collapses within abandoned underground coal mines in the area, although that was not yet certain.
The reserve and surrounding area was once the site of the Walton Park coal mine, which operated from the 1870s and left behind a network of interconnected but deteriorating tunnels when it closed in the early 1900s.
The mine was one of many lying, sealed up and largely forgotten, under parts of Fairfield and the wider Green Island area, many of which dated back a century or more.
GeoSolve had recommended further investigation of the cause of the sinkholes, as well as the risk to the general area.
Alternatively, the council could opt for remedial work to fill and monitor the sinkholes, but would need to "accept the risk of further failures in the wider area", GeoSolve said.
The council had opted for the latter approach, as the sinkholes did not appear to be getting worse.
