Amethyst engagement rings? Absolutely! Diamonds may be a girl's best friend, but Amethyst engagement rings are a unique, original, and a far more affordable choice. As the gem of peace and tranquility, amethyst is mesmerizingly beautiful. A durable and affordable gem, an amethyst ring is excellent for every day wear. Sapphire is the birthstone of September, and pink sapphire is a very popular gemstone in jewelry today. The bright and happy color of a pink sapphire ring is both playful and trendy.