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MB3 93b: Eved Knaani and Shabbos (304:1)
A full-fledged eved knaani (מל וטבל לשם עבדות) cannot perform melacha on Shabbos, even if he is doing it for himself. The master is required to ensure that the eved knaani doesn't perform melacha on Shabbos.
What about a melacha d'rabbanan?
An eved knaani doing melacha on Shabbos for a Jew who isn't his master or for a חולה שאין בו סכנה.