After going through every Roman Emperor, I found only fivesix who served over a year and did not have a bust or statue in known existence. Here is the list:
My basic methodology for finding this list was
Open every emperor Wiki page who served over one year and hope Chrome doesn't crash
Close every tab with a bust or statue of the emperor present
Google the remaining twenty or so
Advanced search the remaining dozen-ish
And I arrived at these fivesix here.
This is hardly a doctoral thesis, so if anyone finds a bust or statue of one of these men, just remove him from the list and leave a comment explaining where you found the statue/bust.