Is it possible to get them to last to the present? Libya gets discussed semi-regularly because the oil makes them a sexy ATL. How about these two comparatively obscure colonies?
Italy IIRC had around 80,000 people in Eritrea by 1940, and I don’t recall the Somaliland numbers, but know that some Italian administrators allegedly considered it home by the end of the UN mandate. Both colonies had small populations, but that will change somewhat as increases in life expectancy occur, and even with rapid increases in literacy/economic condition/lifespan/access to contraceptives it could take several generations for TFR to fall to below the replacement rate.
What conditions are the biggest detriment to greater Italian settlement? Would greater investment, the emergence of new technology to fight tropical disease, and air conditioning be sufficient? And can they partially assimilate the locals after they begin their true demographic boom, to the point of maintaining the colonies even with the ethnic Italian share of the population likely taking a big decline in the final third of the 20th century?
Would a scenario with a neutral Italy in WWII and no Ethiopia invasion do it? I would assume that no joining the Axis and no Ethiopian occupation would be required.
If Italy discovers Libyan oil by fluke around 1916 and begins setting up infrastructure by 1919, stays neutral in WWI until the final months selling to both sides, stays neutral in (a) WWII until the final months selling to both sides, and stays out of Ethiopia, does that do it?
Also, how much priority is Italy likely going to give these?