The problem with writing a believable alternative history is that you have to be pretty clued up with the actual historical period in which your story is set. I would consider writing about an alternative history for a period with which you are knowledgeable or least one in which you would enjoy studying.
If it's alternative American history, you have absolutely tons of subjects to choose from 1940s-60s: World War II, Korea, Suez, Vietnam, Bay of Pigs, Cuban missile crisis, Korea, Vietnam, Cuban missile crisis, Rosa Parks, space race, McCarthyism, Moon landing, cold war, assassinations of JFK, Martin Luther King and Malcom X - even the birth of rock and roll. Many of these events were tied up with, or as a result of others of these events - so changing one could have a domino/butterfly effect on the others.