For the CIE1931 XYZ tristimulus values and x y chromaticity coordinates, I think these are unitless quantities. I have checked different plots of these quantities and haven't seen their units labeled, but could you please confirm that they are unitless?
XYZ measures the perecieved input of a human, not a physical quantity. So yes the data does not really have a unit as such. Mainly because there are so many variables such as what part of the eye was used to observe the color. Secondly because there is no unit for a intensity distribution of light. So its more like asking for a unit for a shape of a car which can not be described by a simple description.