This should be hard to determine. The population of the earth is growing so on average the daily deaths increase even without a special event. In recent times about 150.000 people die each day with a population of more than 7 billion. Furthermore natural disasters effect more people because of higher density. The population on earth increased rapidly during the last decades which means that the "normal" daily deaths are far higher today than lets say during the second world war, this rules out a day in the far past i guess especially since records from far back are unreliable in nature when it comes to numbers. The atomic bomb on hiroshima is possibly the deadliest day of ww2 but the fighting in Europe already stoped at this point. This is likely the most significant daily spike in deaths which wasn't caused by natural disaster. But during the 40s "only" 50.000 people were dieing on average just because the overall population of the earth was far lower.

The actual day with the highest death toll is certainly a day with a natural disaster but these disasters, as you can imagine, result in chaos and its impossible to know what exactly happened and what damage was done on one particular day. Asia with highly populated coast regions suffered many gigantic disasters. The tsunami of 2004 would be my guess.

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