Jones's men open their end-of-year campaign against South Africa at Twickenham on November 12, having won all of their nine previous tests under the Australian.
Coetzee, like Jones appointed after the World Cup, has had a far more difficult 2016.
South Africa, only beaten by two points in a World Cup semifinal loss to eventual champions New Zealand, have lost four of their last five tests.
Their most recent outing saw them suffer a record 57-15 defeat in Durban by the All Blacks, a team they have traditionally rivalled for rugby union supremacy.
In trying to catch New Zealand, who recently set a new world record for a major rugby nation of 18 successive test wins, Coetzee has had to take South Africa's racial politics into account.
During the apartheid era only white sportsmen, with the odd exception, were allowed to represent South Africa.
As a result, high-profile sports such as rugby union and cricket have made moves to field teams that more accurately reflect a country where 90 percent of the population is black.
The policy has not always been stated explicitly, but in March the South African Rugby Union backed a government demand that half the 2019 World Cup team be black.
Whether such an approach is good for South African sport remains a matter of intense debate.
