Justin II and Tiberius II Constantine
September 26 578 through October 5 578

The shortest reign/joint reign in all of Roman/Byzantine history, only 9 days.  It is amazing that there are even any coins produced from this period (or about the period immediately afterward.)  Tiberius II had been making the decisions for the empire for the last four years, and this joint reign was more of a formality of accession than of practical need.  Needless to say the coinage of this period is exceedingly rare.