Women wearing rings of metals other than gold and silver

It is permissible for women to wear rings of gold or silver with diamonds or other precious stones such as emeralds, rubies and carnelians, or of iron if they wish, because the basic principle is that they are permissible and there is no text to suggest that any of that is not allowed. 

It is not makrooh to wear a ring of iron. See the answer to question number 105400. 

Ibn Qudaamah (may Allah have mercy on him) said: It is permissible for women to wear jewellery of gold, silver and gemstones according to their customs and traditions, such as bangles, anklets, earrings and rings, and what they wear on their faces and on their necks, arms, feet, ears and so on. End quote from al-Mughni, 2/324. 

It is stipulated that there be no extravagance involved in that. 

Al-Nawawi (may Allah have mercy on him) said: Our companions said: All kinds of jewellery are permissible for women; it is only permissible so long as there is no obvious extravagance involved. End quote from al-Majmoo’, 5/523. 

And Allah knows best.