Here is a free copyright list of the Western Systems.  In 1912 in Kansas, the U.S. National Association of Jewelers agreed with the pairing of birthstones and crystals with months of the year and signs of the zodiac.

Month                 Birthstone

January              Garnet

February             Amethyst

March                 Aquamarine, Jasper, Bloodstone
           
April                   Sapphire, Diamond

May                   Emerald, Agate

June                   Pearl, Emerald, Moonstone

July                    Ruby, Onyx

August               Peridot, Carnelian

September          Sapphire

October              Opal, Aquamarine, Tourmaline

November           Topaz

December           Turquoise, Lapis Lazuli, Ruby