When the first atomic bomb was to be dropped on Japan Hiroshima was the primary target and the cities of Kokura and Nagasaki were the secondary targets. If Hiroshima had been obscured by clouds the B29 ‘Enola Gay’ would have gone to one of the secondary targets.
For the second attack, Kokura was the primary target and Nagasaki the secondary. As the B29 ‘Bockscar’ approached Japan a weather reconnaissance plane reported that Kokura was clear of clouds. Before making its attack Bockscar was supposed to rendezvous with two observation aircraft, The Great Artiste and The Big Stink, over Yakushima Island.
Bockscar found The Great Artiste at the rendezvous point, but not the other aircraft. After circling for about 40 minutes Bockscar and The Great Artiste flew to Kokura. After exceeding the original departure time limit by a half hour Bockscar arrived late over Kokura.
The delay had resulted in clouds and smoke from fires started by a major bombing raid on nearby Yahata the previous day obscuring the target. Additionally, the Yawata Steel Works intentionally burned coal tar, to produce black smoke. The clouds and smoke resulted in 70% of the area over Kokura being covered, obscuring the aiming point.
Bockscar made three bomb runs with open bomb bay doors and then, with fuel running low, the planes headed for their secondary target, Nagasaki. Bockscar had a problem with one of its fuel tanks and was low on fuel. Otherwise it might have waited longer over Kokura.
The Air Force Magazine has a fuller account of the events.