The emerald's most systematic astrological role is not Western. In jyotisha, the Indian astrological tradition, emerald is panna, the gem of Budha, Mercury, and it is one of the navaratna, the nine gems, each assigned to one of the nine grahas.
The navaratna scheme is worth setting out because much of the gem material in circulation derives from it without saying so. The nine are: ruby for the Sun, pearl for the Moon, red coral for Mars, emerald for Mercury, yellow sapphire for Jupiter, diamond for Venus, blue sapphire for Saturn, hessonite garnet for Rahu, and chrysoberyl cat's eye for Ketu. Rahu and Ketu are the lunar nodes, not bodies, which is why the scheme has nine members rather than seven and why it cannot be mapped onto a Western planetary list without remainder.
This is a coherent, internally consistent system with a substantial textual and commentarial literature behind it, and it is still in active practical use: gems are prescribed by astrologers on the basis of a birth chart, with specific requirements about weight, metal, finger and the day and hour of first wearing. Whether or not one credits it, it is a living tradition with rules, not a modern assemblage.
Two cautions. The navaratna assignments do not agree with Western planetary gem lists, and where a modern source gives a stone a planetary ruler without saying which tradition it is drawing on, it is often silently mixing the two. And the antiquity of the full nine-gem scheme in its present form is less certain than usually implied; the gems appear in classical Sanskrit sources, but a fixed canonical navaratna set is harder to date than the confident presentations suggest.