For pure random, you can just set one layer in the Multi Shader, make sure it has any color selected (is not just in the range of white to black) and then use Hue Random so that it generates a different color for each object or instance etc. For small variations (e.g. different greens so each leaf is a different color on a plant), set the color to the main color you want, and use small Hue and Gamma variations to get different shades and darknesses of that color.
Or to have it randomly sample a result from a gradient so that you control the range of colors that are created, set it to a near white, use Gamma randomization (giving a random greyscale result), and plug that into the C4D Colorizer set to Lightness so that the black to white greyscale is transformed into a color gradient of your choosing.
File attached with some examples.
(Note, saved from R25, using Corona 8 daily build Nov 11, but will work fine in Corona 7 as an approach :) )