I think for their survival, Mohammad Reza Pahlavi must be eliminated by his death between 1975 and 1978 (he was very ill)
Or make Gerald Ford run for a second term and win in 1976, and for fear of losing another ally after South Vietnam, he persuades the army to depose the Shah and appoint his son
(There was a story in Iran about the army preparing for a coup, overthrowing the Shah and appointing his son, but Carter prevented the coup)
Now we look at the implications
Deposing the Shah will empty the revolution of its goal to a large extent, especially if the army promises to restore democracy and reduce the powers of the Shah with the support of Princess Regent Farah.
Khomeini will die in exile and forgotten in France, or the army will kill him, often with other opponents
Without Khomeini, Saddam would not find a reason for the invasion, and therefore there would be no Iraqi-Iranian war, and this is a good thing, and he will continue to flourish and become a leading country in the Middle East.
(It would have become the first welfare state in the Middle East and became the first to completely eradicate illiteracy)
It will be a good thing for Saudi Arabia, because there is no Juhayman Al-Otaibi incident, and therefore no conservative reaction, and also no Muharram uprising, and therefore no very hostile reaction towards the Saudi Shiites.
This means a peaceful era for King Khalid, and Saudi Arabia in the 1980s will be more like the current Saudi Arabia, and it may mean early reform.
The 1977 coup does not happen in Pakistan and Zulfiqar Ali Bhutto remains president and I will not hand him over to Pakistan (Pakistan will remain secular)
The 1980 coup does not take place in Turkey, and Bulent Ecevit remains the prime minister of Turkey, and this means a better situation for the Kurds, and there is no ban on their language, and the 1997 coup may not happen.
Economically, Iran will suffer due to the political turmoil, but after the country is transformed into democracy, the economy will recover and flourish
By 2022, Iran will become one of the 20 countries with an economy between the OTL level, the economy of Italy, the economy of South Korea and Argentina
Socially a mixture of OTL Turkey, Saudi Arabia, UAE and Pakistan
Politically similar to Morocco and Jordan (constitutional monarchy, but the Shah monitors and prevents any foolishness of the government)
The Lebanese war is shorter without the 1979 revolution, and Musa al-Sadr does not disappear
Assuming the fall of the Soviet Union
Iran will take this opportunity to expand and make the independent states puppets of Iran (annexation of Azerbaijan and Armenia and the imposition of puppet regimes in Georgia, Uzbekistan, Tajikistan and Turkmenistan
The United States may not support the Mujahideen in Afghanistan and leave Iran to work, so an Iranian invasion of Afghanistan to restore stability is possible (the restoration of King Zahir Shah will happen often).
The prime ministers will be completely different, except for Abu al-Hasan Bani Sadr, I see him becoming prime minister (he has opposition capital)
The other is Mahmoud Ahmadinejad (a populist), and these are the only two whom the ayatollahs tolerated being elected by the people
Also, Mir Hossein Mousavi, who caused the crisis of 2009, sees him in an alternative reality as prime minister