Yes, in the Twilight series, there are several other vampire covens besides the Cullen family and the Volturi. Some of these covens are mentioned briefly in the books and expanded upon in other companion materials. Here are a few notable vampire covens:
Denali Coven: The Denali coven is a coven of "vegetarian" vampires, similar to the Cullens. They reside in Denali, Alaska. The coven is made up of Tanya, Kate, Carmen, Eleazar, and later, Garrett. Tanya is a close friend of the Cullen family and plays a minor role in the series.
Egyptian Coven: The Egyptian coven is an ancient vampire coven hailing from Egypt. It includes Amun, Kebi, Benjamin, and Tia. Benjamin possesses a unique power to control the elements, making him a valuable asset to his coven.
Romanian Coven: The Romanian coven is another ancient vampire coven, with its members being among the oldest vampires in existence. They are mentioned in the series but do not play a significant role in the plot.
Irish Coven: The Irish coven consists of Siobhan, Liam, and Maggie. Siobhan has the ability to change the outcome of events through her thoughts, making her a powerful member of the coven.
Amazon Coven: The Amazon coven is a coven of vampire women from the Amazon rainforest, including Kachiri, Senna, and Zafrina. Zafrina has a unique ability to create powerful visual illusions.