What kind of eggs dye the fastest?

Color has little to do with how fast eggs will dye. The speed of dyeing depends on the quality, strength, acidity and chemical composition of the dye. More concentrated dyes will dye faster. More chemically compatible dyes (acid rather than alkaline) will dye faster. In the past, eggs were colored with dyes made from natural substances: berries, onion skins, grasses, bark. These dyes worked very slowly, sometimes taking an hour or longer to dye an egg. Today, modern chemical dyes are used instead. Food-grade dyes are used for making eggs that will be consumed. You can increase the strength of these dyes by adding a little bit more vinegar, by adding another dye tablet (e.g. Paas), or by adding several drops of liquid food coloring. The strongest egg dye colors can be obtained using aniline dyes, which are NOT food-grade. Eggs dyed with aniline dyes SHOULD NOT be eaten. These dyes act the most quickly; most will act within minutes, and some will give the desired color within seconds. You must pay close attention and keep an eye on your eggs when using these dyes. The Ukrainian art form of decorating eggs with wax and dye to create "pysanky" traditionally used natural dyes, but today most practitioners of the art use aniline dyes. Pysanky are not meant to be eaten; they serve talismanic and decorative purposes. You can find out more about pysanky by browsing the category "Pysanky Egg Art" here on Wiki Answers, which is found under Hobbies and Collectibles/Arts and Crafts.