Since Rome is now restricted to 2 civil wars, during their third major crisis they now have a collapse to core, which is even worse than a Roman civil war.
This.
Goguryeo's UB, Hanbok Maker, is a Weaver, but Weavers can no longer be built.
@srpt: Fixed the city name map (with the one I linked)?
Also:
Some ideas for UP, UU, UB:
1) Ostrogoths: I hear much about their tolerance of Catholicism despite being Arian. Some kind of happiness bonus for religions could be the UP. For the UB, I suggest
Arian Baptistery to replace Christian temples or monasteries. UU could be a swordsman with Discipline (and/or Formation) bonus, since they are reputed to have better organisation and logistics than other Germanic armies (due to the Ostrogothic kingdom's similarity to previous Roman rule).
2) Visigoths: UP: +50% production of settlers. I derive this from the claim that the Visigoths were the only Germanic invaders to found new cities during late antiquity. UB I have no clue. UU could be a Gothic lancer (a lot of art for such a unit exists on the forums).
3) Vandals: the first things that come to mind are, of course, naval. I would avoid plunder-oriented 'uniques', as it would continue the 'vandalism' stereotype of that people. UU...fire ship?
Fire ships were also employed by the Vandals in 468 against the armada sent by the Eastern Roman Empire.
UB could be a harbour or the like. UP could be a navigation bonus, perhaps.
4) Lombards: I'd give them some kind of buffed spearman UU, some sort of militia or local garrison. UP could be related to the higher number of freemen:
The freemen of the Lombard kingdom were far more numerous than in Frank lands, especially in the 8th century, when they are almost invisible in surviving documentary evidence.
Perhaps a

or

bonus to cottages, workshops, or some sort of percentile change in either.
UB: it's not glorious, but we could turn the market into some kind of food bonus prairie...
The urbanisation of Lombard Italy was characterised by the città ad isole (or "city as islands"). It appears from archaeology that the great cities of Lombard Italy — Pavia, Lucca, Siena, Arezzo, Milan — were themselves formed of minute islands of urbanisation within the old Roman city walls. The cities of the Roman Empire had been partially destroyed in the series of wars of the 5th and 6th centuries. Many sectors were left in ruins and ancient monuments became fields of grass used as pastures for animals, thus the Roman Forum became the campo vaccinio, the field of cows. The portions of the cities that remained intact were small, modest, contained a cathedral or major church (often sumptuously decorated), and a few public buildings and townhomes of the aristocracy. Few buildings of importance were stone, most were wood. In the end, the inhabited parts of the cities were separated from one another by stretches of pasture even within the city walls.
It isn't the best list of UUs/UPs/UBs, but after spending a whole day of off-and-on research, it's the best I can come up with.
edit: Honestly, I'm not sure if the whole "heavy spearmen -> swordsmen -> heavy infantry" progression of units is exactly the way to go, considering what late antique armies actually were. I wonder what everyone else's thoughts are on this.
@srpt: the Romans declared war on me. Then, all of a sudden, I lost Babylon to the Romans, whose troops I did not see in the area, and I did not get any invaders elsewhere, so either the invaders just didn't come and they happened to be near Babylon at the time (which means there's still a bug), or that the invaders appeared, but near Babylon.
edit:
"An independent city has fallen under the protection of Rome" event occuring well past the Byzantine spawn. This should be disabled by 330 AD at best.