Existed from May 1835 to 1842 when South Australia became a crown colony. Its functions were continued by the Colonial Land and Emigration Commission established in 1840, with some overlap of functions during the years 1840-1842.
National Archives (UK) website, viewed November 6 2020 A Colonial Land and Emigration Commission was created in 1840 to undertake the duties of two earlier and overlapping authorities which were both under the supervision of the secretary of state. These were the Colonisation Commissioners for South Australia, established under an act of 1834, and the agent general for emigration, appointed in 1837. The new commission dealt with grants of land, the outward movement of settlers, the administration of the Passenger Acts of 1855 and 1863 and, from 1846 to 1859, the scrutiny of colonial legislation. https://discovery.nationalarchives.gov.uk/details/r/C4577
South Australia Original Correspondence in Records of the Colonial Office as scanned by AJCP. Viewed on Trove, 9 November 2020 Orders and land regulations of the South Australian Colonization Commissioners, 1835 - 1840 and Original Correspondence South Australian Commissioners, 1842 https://nla.gov.au/nla.obj-728202791