Maybe use the Divisio Regnorum from 806. This is a division between the three sons of Charlemage, which lived at that point. You could also slightly modify it.
So either prevent the death of his sons Pippin and Charles/Karl, or kill Karl the Great shortly after this plan.
After that, you need to kill either Ludwig or Pippin or their successors without any heirs, and help the other southern kingdom to gain control of the heritage.
Here is a beautiful map including the Divisio Regnorum from 806 from Ian Mladjov (an historian with many beautiful historical maps on his website):
(Mladjov allows the use of his maps under the following circumstances: "Given proper attribution, these maps may be used freely for non-commercial educational purposes.")
https://sites.google.com/a/umich.edu/imladjov/maps
Problems: Further partitions, if the three sons die with several male children. Here are some possibilities.
If Pippin has two heirs, we would see a further division between Italy and Bavaria.
If Pippin has three heirs, you need to give one son Bavaria, and the other two would rule over a divided Italy, which has some idea of unity (because of the former langobardic kingdom), which would lead to even more conflicts.
If Ludwig has two heirs, we would see a division between Aquitannia and Burgundy,
If Luwig has three heirs, we would see a division between Aquitannia, Burgundy and Septimania.
If Karl has two heirs, we could see a division between "Neustria" and an East Francia.
If Karl has three heirs we could either see a division between Neustria, (Large) Alemannia and East Francia, or between Neustria, Austrasia and (Large) Saxony/Thuringia
If Karl has four heirs, we could see a division between Neustria, Austrasia, Alemannia and (Large) Saxony/Thuringia
If a king dies without heirs, the neighboring kings would fight to gain control, which could either lead to the partition of the kingdom without clear succession, or one successful, powerful king.
(Conquest, marriage and so on could complicate this process)
The pope would crown the ruler of Italy as emperor. But in this scenario, the title of emperor wouldn't mean more power (but prestige) compared to the other kings.
If you want to prevent further partitions, kill the Karolingians as early as possible. If the elites of these kingdoms begin to elect new non-karolingian kings, a partition could become stable for the next centuries (as long as the resulting kingdom is large enough but not too large).
Now, look at the three kingdoms, and their possibilities.
The realm of Ludwig would probably focus on the Umayyads. This kingdom could conquer territories on the other side of the Pyrenees, and become a Mediterranean power (if capturing the Balearic Islands). The region of Arles or the region around Toulouse would make a great center of this kingdom. If Italy is weak, a king of the Realm of Ludwig could cross the Alps, to travel to Rome. I see possibilities for trading towns at the coast of the Mediterranean. If there is no personal union or control over Italy, this kingdom is not to large, so a strong king is possible.
The realm of Pippin would face the Eastern Roman Empire in the South. At the same time, this kingdom would give the king an easy possibility of becoming Emperor. But this title and territorial ambitions could lead to some conflicts with the Romans (Byzantines). Hungarians could invade (as in OTL). Also an islamic conquest of Sicily could threaten the kingdom.
If you want to control Bavaria, you need to travel through the Alps. Bavaria would probably develop strong autonomy.
In Italy the relationship between king/emperor and pope is essential. Several results are possible (king controls pope, and rules in Rom -> More imperial ambitions; king and pope coexist, king has his power base in Northern Italy, and the pope is in Rome; Pope is more important than the king, or helps usurpators/local elites etc. -> Pope rules Rom, unstable northern Italy).
Italy was in OTL during the late Karolingians really really unstable (but I currently don't know the exact reasons). But some expansion (for example Southern Italy or Dalmatia) seems possible.
The realm of Charles/Karl is the largest and probably the most difficult kingdom. Wikings could invade the coast. If a king failes to defend the realm from them (as in OTL Charles/Karl the fat), this would weaken his position. At the same time, hungarians could invade the eastern border of this kingdom. Conflicts with the Slaves would probably also occur. The king can't be at the same time at the Eastern border and at the Atlantic coast. The main power base would be at the old core lands of the Francs, but the king needs to travel far greater distances than in the other two kingdoms. Alemannia would be a region without many royal visits, therefore with large autonomy. Powerful counts could become dukes over large territories, defending them from invaders. This could reduce royal power. The kingdom is to big for further expansion. The result would be a Holy Roman Empire without the title of Emperor. But if several dukes declare themselves king, the whole thing would split into various smaller kingdoms.