Like the Shah of Iran, it was Haile Selassie's efforts to "modernize" his country that undid his regime more than anything else. The "pillars" of the Ethiopian monarchy were, and always had been the support of the landed elite and the Orthodox Church. The support of the former was undermined by Land and Tax reform, while the hold on the latter on the average person was undermined by sending students abroad.
According to Odde Arne Westad's The Global Cold War,most of the intellectual disillusionment with the Monarchy came from Ethiopian students who had studied abroad in the West, especially in the US. Rather than just learning the technical skills that they had been sent to study, many also became attracted to the ideas of Marxism and the New Left. The young people Selassie's government had in many cases sent to the West on the country's dime to revitalize it became far more interested in destroying it.
To survive the 1970's, the Selassie regime would have had to one of several things differently. They could have attempted to keep the country as insular as possible, slowly introducing modern technology while doing their utmost to preserve traditional institutions and culture. Alternatively Selassie could have simply instituted a more thorough "coup-proofing" strategy for his regime. The unsucessful 1960 coup could have served as a wake-up call. He could have staffed his military only with members of his extended family, and recruited only from his own Amhara ethnic group.
As backward as some of those measures may have made the Selassie regime appear to the outside world, they would have made any attempt to depose him much more difficult.
The easiest way to keep Ethiopia a monarchy though would be to somehow to prevent the 1973 Arab Oil Embargo, which triggered high gas prices and inflation, and was the proximate cause of the civil unrest that led to the formation of the Derg. Selassie probably would have died in a few more years, and his son Amha Selassie would succeed him. The monarchy would then have then developed along the lines of the Saudi or Morrocan Royal government, and be something between an absolute and constitutionalism monarchy today. If they had taken the isolationist path I outlined above they would probably be more of a cross between Saudi Arabia and the Congo under Mobutu, though far more civilized than the later and less fundamentalist than the former.