One pivot point would be to have the Carter sufficiently call out the Shah of Iran in 1977 or 78' on his human rights record, to the extent that it displaces the takeover of the US Embassy in Tehran. The anger from the Shah coming to the US for cancer treatment helped fuel emotions that drove the Embassy takeover. The subsequent and ongoing hostage situation became a nightly news leader going into the 1980's election and a definite drag on Carter's public image. The Iranian Revolution was going to happen anyway, and the US intelligence services misread it's extent and the accompanying anti-American feeling. I'm not sure how you pull off that change without 20-20 foresight though. Plus that rejection of an old ally (the Shah) would have had American conservatives in an uproar about the US stepping back from commitments.
The Iranian Revolution also lead to yet another disruption in oil deliveries that upset world oil prices to the extent it caused significant financial problems in the developed world. Perhaps again with 20-20 foresight, have Carter be more proactive and extensive in releasing US oil reserves to stabilize supply and pricing, partly offsetting world financial displacements.
My own personal wish in the wake of the second oil crisis ('73 & '79)- that Carter would have announced the US will launched an accelerated alternative energy development project on par with the space program, so in decades to come the US is less dependent on fossil fuels. To be absolutely sure, in 1979 that idea would have sent Carter to the showers, and oil and coal state Representatives and Senators would have lined up to lynch Carter. It should have been done anyway for the good of the country and the world.