Most Scarce Roman Emperors?

Any Western emperor after Honorius is rare in the English-speaking world, mainly because Honorius was the guy in charge when Rome evacuated from Britain. So coins of post-Honorius emperors are almost never dug up in Britain.

As for the "mainstream" (i.e. non-usurper) emperors, as a general rule the briefer the reign, the rarer and more valuable the coinage. Didius Julianus, the man who purchased the emperorship when the Praetorian Guard held an auction for it, only reigned for two months in 193 AD (the "Year of the Five Emperors"); he is probably the scarcest of the Five as his rule was largely unrecognized outside Rome itself and virtually none of the army was in his pay.

Balbinus and Pupienus, joint co-emperors elevated by the Senate in a panic when their previous candidates, Gordian I and Gordian II, both fell in battle to Maximinus Thrax in AD 238 (the "Year of the Six Emperors"), also ruled for about two months. Coins of Gordian I and Gordian II are also scarce, due to their short reign, though they can sometimes be difficult to tell apart from the much more common coinage of Gordian III.

As you can tell, whenever there was a time known as "The Year of the {insert number larger than three} Emperors", you've got yourself some scarce emperors to find.

Awesome coin! Is this yours?

I recall reading somewhere that Domitius Domitianus holds the record for the latest provincial coin; by the late 3rd century provincial issues had petered out, and Diocletian's reform squeezed out the last ones.
(There are a few Bosporan issues that are nominally attributed to later emperors, but they don't qualify because they don't actually mention which emperor they are under, only the date and the local king.)

Immediate qualification: this is a list for imperial coinage, and does not represent how (e.g.) provincial coins in the name of Tranquillina are relatively common. That aside, however, this is a far better list than some others I've seen.

...though I'd still dispute the position of Valentinian III. How come he's always so darn low in those lists? I didn't think his coins are anywhere near that rare. He's placing lower than Johannes, for ch*rping's sake, and Johannes is pretty famously rare. Did I miss something?
It can't be the "pulled out from Britain" thing, because Johannes had a very short reign that was immediately followed by Valentinian III's much longer one, and both were after Honorius.

(I don't get how Marcian managed to place above Leo, either, but that might be just me... I had half a dozen Leo coins before I could find myself a Marcian. And in that case it could just be that the earlier types were more likely to end up in the west.)

In terms of official emperors (which I define as those ratified by the Senate and generally unopposed by any official authority), I believe Olybrius takes the cake, with only 12 or 13 known coins across all denominations, most of which are in museums. Romulus Augustus isn't much more common, but usually brings strong six figures due to the romantic association of his abdication to the official beginning of the Dark Ages.

In terms of usurpers, there are a few unique ones of dubious quality, but Domitianus II, Saturnius, and Silbannacus are all known from two coins each and are accepted to be authentic coins of a real individual.

With late bronzes, familiarize yourself with the Constantinian dynasty, the Valentinian dynasty, and the Theodosian dynasty- all members of those (except Nepotian and Hanniballianus) are common, and basically everyone else is scarce to rare.

Past Honorius, the main challenge is that most rare emperors issued the same types as common emperors, and rarely have more than just a couple visible letters. I have a small bag of "maybe Johannes" Victory type AE4s which could also be Valentinian III, Honorius, Theodosius II, etc.

The *really* rare ones mostly did not issue bronze at all, just gold and sometimes silver. The odds of finding a Jovinus or Petronius Maximus unattributed in a collection is incredibly slim, but I suppose not impossible.