This page uses the CMC(I:c) color differencing algorithm to procedurally generate a set of visually-distinguishable colors within a certain tolerance. To begin, specify the set of colors to search through by changing the values below, and then click on the "Refine" tab above.
During refinement you can choose whether or not to randomize the search through the color space and (more importantly) change the perceptual thershold to generate more- or less-distinct colors. When you have a good set, click on the "Results" tab to perform final sorting and to get your list of colors.
To best support individuals with colorblindness (deuteranopia or protonopia) keep a set to 0; vary only L and b.
Here are your results. Sort and shuffle them as you see fit. (Interleave of 1 leaves the values sorted; given the default sort by HSV, I personally find that an Interleave value of 5 produces a pleasing set of color ordering.)