This is how I do it. First define this function to that you can apply or insert a color with a single button:
colorPasteButton = Button[" ",
ib := InputNotebook[];
If[NotebookRead[ib] === {}, Paste[ib, #],
FrontEndExecute[{FrontEndToken[ib, FontColor, #]}]],
Appearance -> "Palette", Background -> #, ImageSize -> Full] &;
Then, create your palette in the notebook, for example:
Pane[
Grid[
{
{Tooltip[colorPasteButton[Black], "Black 100%"],
Tooltip[colorPasteButton[GrayLevel[0.15]], "Black 85%"],
Tooltip[colorPasteButton[GrayLevel[0.50]], "Black 50%"],
Tooltip[colorPasteButton[GrayLevel[0.75]], "Black 25%"],
Tooltip[colorPasteButton[GrayLevel[0.85]], "Black 15%"]}
},
ItemSize -> {2, 1}, Alignment -> Left, Spacings -> {.1, 0}],
FrameMargins -> 5]
Then convert it to a palette:
CreatePalette[%]
And finally go to the Palettes menu, and select "Install palette".
If interested in learning more about the colorPasteButton see:
https://mathematica.stackexchange.com/questions/95243/paste-set-color-with-a-single-button-for-palettes?form=MY01SV&OCID=MY01SV