I read about an account written by a Catholic that talked about Byzantines having automatons inside their throne-room. I can neither find the book that I read it from or find the Bishop that gave the account, so I am obviously wary of citing it when speaking about Byzantine technology.
So, my question is; did the Byzantines, (Or did said Bishop report that they) have things such as that? And if so, can you point me to sources?
Yes! The Byzantines (and medievals in general, I think) were really fascinated by this kind of thing. You're probably thinking of Liutprand of Cremona's Antapodosis 6.5:
In front of the emperor’s throne there stood a certain tree of gilt bronze, whose branches, similarly gilt bronze, were filled with birds of different sizes, which emitted the songs of the different birds corresponding to their species. The throne of the emperor was built with skill in such a way that at one instant it was low, then higher, and quickly it appeared most lofty; and lions of immense size (though it was unclear if they were of wood or brass, they certainly were coated with gold) seemed to guard him, and, striking the ground with their tails, they emitted a roar with mouths open and tongues flickering. (Trans. Paolo Squatriti)
Liutprand was a Catholic bishop who was relatively familiar with Byzantium, so his writings have a lot of anecdotes showing the exotic features of Byzantine court life. Such automata are also mentioned by Constantine VII in the Book of Ceremonies 2.15 (though they behave slightly differently). Both of these works are available in English translation:
You may also want to check out a very recent book specifically on medieval automata, which mentions both of these accounts in a broader context: