Two birthdays ago, my brother gave me "Byzantium: The Early Centuries" by John Julius Norwich (Penguin Books, 1990). It's a general history of the Late Roman and Byzantine Empire from the accession of Constantine to the Empress Irene (330-802 AD). It's apparently the first of a trilogy (the other parts being "The Apogee" and "The Decline and Fall") and it's quite readable. It's a general historical work and not just about the emperors, of course, but since the emperors are the ones that authorized the histories, most of the book is indeed about them.
If you don't have it yet, and are interested in Byzantine coins, get Sear's "Byzantine Coins and Their Values". Like his Roman catalogues, Sear includes a brief bio of each emperor in the introductory section before listing the coins.
