I did some searching, and I can confirm that it is quite difficult to turn up illustrations depicting specifically Oyo cavalry.

One possible way to get some idea of what Oyo cavalry might have looked like is to look at Yoruba cavalry figurines, like these, or these.

Of course, there are some potent drawbacks to that approach. The art is representational, but not photorealistic. Also, pigmentation is very rare, so it can be very hard to determine if areas on the human part of the sculptures is meant to depict metal or leather armor or merely patterned fabric.

On the other hand, some of the depictions of saddles, bridles and stirrups do match closely with this 1960 photograph of a royal horse from Oyo.

Another approach is to look for illustrations and depictions of Songhai, Borno or Fulbe cavalry. The rationale here is that the Empire of Old Oyo built up its cavalry forces by trading slaves for horses from these northern neighbors that had established cavalry traditions. Therefore, we might presume their established cavalry traditions to also have had some influence on the newer Oyo cavalry forces. Influences such as a preference of heavy lance-armed cavalry, rather than bow and arrow wielding light-cavalry (before the widespread introduction of muskets). Of course, we must be careful not to over-estimate the amount of influence, and realize that in personal decoration, armoring or clothing, it is hard to know exactly how closely or differently an Oyo cavalryman would have appeared from one of the Sokoto caliphate or Kanem-Borno.

Although there is not much pictorial material available to show the appearance of Oyo military forces, there has been a good deal of scholarship discussing their tactics and organization.

Robin Law has written works that will be most relevant to your interest. His article A West African Cavalry State: the Kingdom of Oyo in the Journal of African Studies vol XVI (1975) directly addresses the role of horses in Oyo society, the growth of the Oyo cavalry in the late-17th century and the clash with Dahomey.

Two other works by Law, The Oyo Empire c1600-c1836: A West African Imperialism in the Era of Atlantic Slave Trade written in 1977, and The Horse in West African History written in 1980; will also both be relevant. Despite its age, The Oyo Empire continues to be a keystone book for the study of Oyo history.

Other works that might also be helpful are Warfare in Atlantic Africa; 1500-1800 by John K. Thornton. He spends some time on the Oyo-Dahomey conflict, examining the tactics of each side, as well as its implications for the Atlantic Slave Trade. Of course, much of the work is dedicated to Songhai, Asante, and Kongo military history.

Also, Warfare & Diplomacy in Pre-Colonial West Africa by Robert S. Smith is possibly useful. Again, the author's interest is directed more towards Mali, Songhai, the Fulani jihad-states, etc. So, talk of the Oyo military will only be lightly touched on.

Edit- One more source. Yoruba Warfare in the Nineteenth Century by Michael Crowder and J. F. Adi-Ajayi. It is directly focused on your interest, and Crowder and Ajayi are highly-regarded scholars of West Africa. However, this book is from 1960, so treat their conclusions with caution. There have been more than 50 years of archaeological work, and at least two generations of West African historiography since this work was published.