My answer to the problem is to devastate anyone else who would try to get the bomb before Italy.
So...here goes.
WW2 goes much as it did in OTL, except without Italy's involvement, meaning Barbarossa goes off sooner, yadda yadda, European Russia is conquered, but Germany remains involved in a horrific (from logistics, weather, etc.) war with Soviet remnants led by our stereotypical Stalin replacement, Zhukov.
The US enters the war on cue, and focuses on the Japanese theater, since an invasion of France into the teeth of the army that conquered Russia seems...not brilliant. The US defeats Japan earlier...too early, in fact, because Japan has to be conquered with conventional weapons, with ensuing casualties.
Just as Japan is defeated, the US gets nukes! Oh joy! Germany gets nuked repeatedly, as the US drops a bomb every time it comes off the assembly time...to avoid an early German surrender, let us say that Germany gets the bomb as well, and manages to deliver all sorts of nastiness to the UK, and possibly America if their rocketwank works. During this time, lets eliminate another future atomic power by having Germany pull its own Morgenthau on occupied France.
Eventually Germany surrenders, and is rather radioactive. Without support from Russia, the Red Chinese cannot force the Nationalists out of China, and China remains in civil war. Now there isn't a country in the world that will get nukes before 1970:
US: First with nukes.
Germany: Second with nukes, is now irradiated and impoverished.
UK: Nuked repeatedly, has Empire to try to hold onto, is under American nuclear umbrella anyway.
Russia: You think the Germans were particularly nice when they were occupying Russia? Or that industry is in a good condition? Think again.
France: Morgenthaued. Busy trying not to starve.
China: Perpetual civil war.
Japan: Close to exterminated.
Italy: It's around 1948, and you have 20 years to develop nukes with a poor industrial base and to keep a fascist regime in power. India did the former, Franco did the latter...get to it!