Enslavement of Native Americans was quite widespread in the colonial period, but this trade ended in the 18th century for a variety of reasons, among them the declining numbers of natives, the rise of the African slave trade, and the fact that what natives remained took greater action to try and prevent their own enslavement and the theft of their land by white settlers.

Other than this, I, too have never come across any mention of a slave who was not either black or a Native American, though of course absence of evidence is not evidence of absence.
Of greater interest might be the way in which the term 'black' has changed over the intervening years. Back then, anyone with any known African ancestry (the going phrase was "one drop of blood") was considered black, and one of the outcomes of this was that there were some slaves who we today would see as assuredly white. The primary reason for this was slave owners raping enslaved women, whose daughters would be slaves and perhaps sold to a different man who might rape them, and so on. The end result of this appalling cycle of sexual violence would be people with mostly white ancestry, who appeared white, who were nonetheless descended from a slave and slaves themselves. Images of these people were used to great effect by Northern abolitionists, as the thought of apparently white people being whipped and raped was much more inflammatory to the average person in the antebellum period than seeing those same things done to blacks.