Scrum-half Cooney kicked Ulster’s winning penalty in the 19-17 win over Cardiff.
It will be one of his last half-back outings with Burns, who moves to Munster at the end of this season.
Addison is named at centre after switching to midfield in last week’s game after Hume was injured.
Ulster’s other absentees include Iain Henderson, Rob Herring and Steven Kitshoff, who has played his final game for the Irish province after sustained a season-ending knee injury in the Challenge Cup quarter-final defeat by Clermont Auvergne two weeks ago.
A bunched battle for the play-off spots has Ulster level on points with Edinburgh and Connacht, who occupy eighth and ninth places, and only a point behind the sixth and seventh-placed Stormers and Ospreys.
After suffering successive defeats against Leinster, Glasgow and Scarlets, Benetton regrouped with home wins over Connacht and the Dragons and they are likely to present Ulster with a tough test at Kingspan Stadium.
Ulster: Lowry; Baloucoune, Addision, McCloskey, Stockdale; Burns, Cooney; O’Sullivan, Stewart, Wilson; Sheridan, O’Connor (capt); Ewers, Crothers, McCann.
Replacements: Andrew, Warwick, French, Izuchukwu, Jones, Shanahan, Marshall, McIlroy.
Benetton: Umaga; Marin, Menoncello, Zanon, Smith; Albornoz, Uren; Gallo, Nicotera, Ferrari; Scrafton, Iachizzi; Izekor, Lamaro (capt), L Cannone.
Replacements: Lucchesi, Nemer, Pasquali, N Cannone, Favretto, Halafihi, Garbisi, Drago.
