There was such an effort. From 1946 until 1948 or so, there were serious attempts in the United Nations to institute "international control of atomic energy," which was at its heart banning nuclear weapons without banning peaceful nuclear technology. Creating the UN Atomic Energy Commission, a committee of states that would negotiate this, was literally the first official action of the United Nations.

The USA and USSR both introduced "plans" for how to do this. The US plan, known as the Baruch Plan, was a modified version of what was known as the Acheson-Lilienthal Report. In brief, it said that the UN would create a new entity (the Atomic Energy Authority) and it would be in charge of making sure that other nations weren't making nukes. It would do so by inspecting their countries for the kinds of facilities (uranium enrichment, nuclear reactors) that would produce fissile material, and possibly have control of uranium mines. The US would not disarm its own nukes until other nations accepted these kinds of controls. It was not a bad plan is not that different from the modern Nuclear Non-Proliferation Treaty in many respects, though it was criticized in its day for focusing too much on inspections/verifications (though in hind-sight, those are crucial to any successful arms control treaty).

The Soviets didn't like the Baruch Plan for a variety of reasons, but one of the big ones is that it required everyone else to be non-nuclear before the US would join them. They didn't trust the US, and thought that the only nation to use nuclear weapons against another nation should be lecturing anyone about how peaceful their intentions were. The Soviets proposed an alternative plan, the Gromyko Plan, which was essentially just a ban on nuclear weapons but lacked any verification or enforcement mechanism. It was dismissed as not a practical treaty by the US.

Neither nation trusted one another enough to really try to make it work. The US effort was always somewhat half-hearted (at least when it came to White House support) and it would have taken extraordinary amounts of good-will to imagine it being passed. The Soviet effort was just rhetoric, not a real plan. The Soviets were, of course, actively seeking a nuclear arsenal in secret at the same time, and the US was, as well, developing and testing nuclear weapons during this time. So neither possessed the level of trust and goodwill to imagine making this work.

In practice, the UN AEC continued to exist technically until the early 1950s, but it was effectively dead in the water by 1948. In 1949, the Soviets detonated their first atomic bomb, and that was that. Many of these same ideas came back in the form of the Nuclear Non-Proliferation Treaty some time later.

Separately, one might also point out the success of regional nuclear weapons bans, which include many regions of the world:

• Treaty of Tlatelolco — Treaty for the Prohibition of Nuclear Weapons in Latin America and the Caribbean
• Treaty of Rarotonga — South Pacific Nuclear Free Zone Treaty
• Treaty of Bangkok — Treaty on the Southeast Asia Nuclear Weapon-Free Zone
• Treaty of Pelindaba — African Nuclear-Weapon-Free Zone Treaty
• Treaty on a Nuclear-Weapon-Free Zone in Central Asia

And there is also the Treaty on the Prohibition of Nuclear Weapons, which has been signed and ratified by many (non-nuclear) states in recent years. So one cannot really say there have not been efforts; there have been many, and some of them were even in motion (albeit in secret) before the bombing of Hiroshima (international control schemes pre-date the use of the bomb).

One might also ask why the efforts at banning chemical and biological weapons were so much more successful than nuclear bans. There are no doubt several possible answers but one that Nixon offered up in private for supporting the Biological Weapons Convention: "If somebody uses germs on us, we'll nuke 'em!" Nuclear weapons were much more primary to the security postures of the nations that have them (and their allies) than chemical or biological weapons ever were.