If the planet Abracadabra is one some astrophysicists insist exist and others insist do not, people in the latter camp cannot at the same time claim they have something to contribute to the body of knowledge (-ology) about Abracadabra. They might have things to say about the beliefs of those that do insist on its reality, but that is not the same.
Hence, there is no definition of theology that would make atheism a meaningful qualifier of it. Starting with wikipedia:
Theology is the systematic and rational study of concepts of God and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university, seminary or school of divinity.
This alone may seem potentially anthropological -- it says "concepts of", and anyone might study someone else's "concept of" something without accepting it and contribute to a body of knowledge surrounding that conceptualization. However, while theology may involve examinations of false conceptualizations of God, the ground of such analysis is the true things that can be said about God, and contributing to the body of knowledge requires either applying an explicit and existing set of truths about the divine or an adaption or elaboration of a set of truths about the divine. That's not an anthropological approach, which would not depend on either the truth or falsity of the divine and simply would be an examination of a belief about it.
While an atheist could study theology along (e.g) anthropological lines, there is not anything a specifically atheist perspective could sincerely contribute to the body of knowledge; this does not mean the individual atheist could not contribute, only that their contribution could not be something that could only be made by an atheist. Atheism weakly defined is a non-belief in God and the divine; more strongly defined (aka. "antitheism") it's a denial that God and the divine exist.1 Either way, there is nothing to know about and therefore no legitimate body of knowledge to consider and no possibility of making legitimate contributions to it.
1. The significance of this distinction is debatable and that debate is beyond the scope of the question, but if "I do not believe in God" is akin to "I do not believe 2 + 2 = 5" and "I believe there is no God" is "I believe 2 + 2 is not 5", then there you are: there's no knowledge to be had regardless of whether God is something you don't believe in or something you believe does not exist.