Ulster left Southern Kings still looking for their first win in the Guinness PRO14 this season after running out convincing 42-17 winners at Nelson Mandela Bay Stadium.
The Irish side ran in five tries in the opening 31 minutes to effectively put the game to bed, although Tertius Kruger and Aston Fortuin responded for the hosts.
Cooney also kicked all six conversions, with Demetri Catrakilis adding a penalty and a conversion for the South Africans.
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