It seems like the most problematic color is the "champagne" or "skin color." I do know that some Michael's and Jo-Ann's carry a tub or bag of mixed color beads, that has red, orange, yellow, green, navy, black, pink, white, and a cream color. I recommend that you use that cream color for skin, if you have it. Glow in the dark orange works well too (thanks for the suggestion 420Monster). You can even use pale pink, very pale yellow, or even white (as long as the eyes don't have white on the outside).
However, if you want to get the colors as close as possible, I recommend that you order the colors you need online. Online stores normally offer a much wider range of colors than brick and mortar stores. One site which has a wide selection of pony bead colors is BeadKraft.