Looking at a cursory search on Wikipedia, it looks like the earliest example of a coin where an emperor who is clearly wearing a crown instead of a laurel wreath is Constantine I, but some of the coins of his father, Constantius I, look a bit ambiguous. Every emperor after them is shown clearly wearing a crown. Was this part of an effort to "de-paganize" the Imperial imagery as part of Constantine's Christianization efforts? If so, why did Justin the Apostate continue this trend? Was this a Germanic tradition adopted by the Emperor that was simply more splendorous than a simple laurel wreath?
You can start here, When did Roman emperors start wearing crowns?, with an excellent description by /u/UndercoverClassicist