The 35-year-old left-arm seamer Payne had played two matches for Sunrisers in the tournament this season but has been force to withdraw due to an ankle injury.
Coetzee has previous IPL experience having represented Mumbai Indians in 2024, taking 13 wickets in 10 matches and with Gujarat Titans last year where he took two wickets in four games.
The 25-year-old played for the Proteas in the five-match T20I series in New Zealand last month, picking up eight wickets to help the visitors to a 3-2 series victory.
Sunrisers have been ravaged by injuries this year, especially to fast bowlers, as England international Brydon Carse was replaced by Sri Lanka's Dilshan Madushanka.
Good news from the Sunrisers camp is that regular captain Pat Cummins has been cleared to join the team after undergoing scans on his back in Sydney.
Sunrisers have won two and lost three of their opening five games so far with their next fixture against Chennai Super Kings at home on Saturday.
Kagiso Rabada took three wickets while Shubman Gill struck 86 to lead Gujarat Titans to a third victory of the season as they beat Kolkata Knight Riders by five wickets in Ahmedabad.
Proteas batter Connor Esterhuizen is set for his first taste of the Indian Premier League after being signed by Gujarat Titans as an injury replacement for the remainder of the season.
Mumbai Indians head coach Mahela Jayawardene says his team need to find a "spark" after they slipped to their fourth consecutive defeat in this season's Indian Premier League.
In a classic Wankhede run-fest on Thursday night, Punjab Kings produced a clinical chase to dismantle Mumbai Indians by seven wickets with 21 balls to spare in IPL 2026's 24th match.
