In ATL where Italy steers clear of WW2, unlikely it may be, the horn of Africa could be the downfall of Fascism. No matter how much money Mussolini would be willing to sink, there never would be enough italian colonists to counter the local population. In effect no european nation was able to keep any part of Africa, short of some costal town. So basically we have two possible scenarios:
1) Mussolini refuse to accept the inevitable and fights on to keep control of Abyssinia. In the end numbers win over the fascist stubborness and Ethiopia becomes indipendent, while the economic crisis caused by the military effort destroy the fascist regime, as happened in OTL Portugal.
2) Mussolini, or his successor, understands that keeping Abyssinia is near impossible and opt to create a few puppet regimes. Playing carefully the several factions against each other, Mussolini could set up an "indipendent" and "free" Abyssinia, Erithrea and Somalia. Each of this nations would keep good relations with Italy, grant few military bases and house few italian regiments, sent there to train the local police/army and guarantee the local goverment against "communist" insurgents.
Mussolini could also go further and steal a page from Great Britain book, setting up an "Italian Commonwealth of East Africa" with Vittorio Emanuele as formal head of the newly established states.
In the former scenario the only points to clarify is how soon the fascist are ejected from East Africa and how bloody is the aftermath. If the ethiopians try to keep the whole AOI as their own, a civil war is going to explode immediately; if they are somewhat more restrained we could have a OTL like situation.
In the latter scenario is difficult to predict how long the italian influence would last: there are simply too many butterflies. But if it last enough, it would cause an awful lot of changes. For example the italians would try to meddle into the first sudanese civil war, with some interesting results...
As for Lybia, though not requested by the OP, the fascists are going to fight tooth and nail to keep the oil. They would flood the place with colonists and then held a "democratic referendum" over the colony fate. A referendum where italians would weirdily be the majority of the voters.
The repression and the forced integration of the arab element would be ugly, but if the italians manage to gain some of the tribes on their side through corruption, they could keep their hands on Lybia (not an easy job, though).
Again, it's interesting to imagine what Italy would have done if it had kept Lybia. I think, for example, that Mussolini would have stickied his nose in the Suez crisis, if not directly in Egypt during the Nasser revolution.