Copper
The presence of copper in the soil surrounding a fossil can create a bluish or greenish tinge. This is due to oxidization of copper that takes the place of organic compounds within the fossil. Just as a copper pot oxidizes when exposed to the air, so too will a fossil bearing copper oxidize to a greenish blue color.
Cobalt
Cobalt is a mineral that has been used since time immemorial for bestowing a blue or purple tint to dyes for fabrics and pottery. Just as cobalt can dye linen, its presence in a fossil gives it a blue or purple color. Cobalt is naturally blue, but turns a purple color when exposed to the mineral chlorine. This same effect is seen in fossils exposed to both compounds.
Manganese
Manganese is a mineral with a natural pink hue. When a fossil is deposited in soil and left there for thousands of years, its organic compounds are replaced by the minerals found in the soil. If the soil contains manganese, the fossil may gain a pink hue, or a washed out off-white color.
Silica
Silica is a compound with a natural white-gray color. Its presence in conjunction with other minerals can create fossils ranging in color from an almost brilliant white to washed-out variations of other colors, such as a blue-tinged white when a fossil is exposed to both silica and cobalt.
Sulfur
Sulfur is often present in soils and stratas where fossils are found. This compound possesses a yellow-white color and discolors fossils that are exposed to it accordingly.
Iron Oxide
Iron oxide-exposed fossils are probably the most commonly found colored fossils. Their red-brown tint looks like rust because iron oxide is rust. Iron in the soil is absorbed by the fossils, which then for all intents and purposes rust when exposed to oxygen, just as a piece of iron would.