The websites I have found give 24-hr rainfall totals, but are not delineated from 0000 to 2400 hrs (whole calendar days). Instead, they relate the metrics from, say, rainfall falling within 1730hrs to 1730hrs on different calendar days, presumably the times when personnel actually checked the gauges.
I do not know of such website, but I think that all depends on the research area you want to study.
The national weather services of a large number of countries have daily data but, as you wrote, is not from midnight to midnight. You should look for hourly data and then add and substract accordingly, even if such data is difficult to find and, sometimes, must be paid for.
Best,
More sleuthing found that Weather Underground, for example, is not suited for generating calendar day rainfall amounts. A better source for that is the NOAA databases. Weather Underground is good for daily rainfall timing, via each day's charts, if the reporting station (usually an airport) is reasonably close to your study site.
Have you tried Wolfram Alpha? It's a computational intelligence site. https://www.wolframalpha.com/
For example, if you were to type in the search bar at the top "Rainfall for December 25, 2016 in Atlanta, GA" It will return the results for you in text and graphical form. There's a dropdown on the right hand side of the graph that allows you to view week, month, year, and 5 years. And then you can hover over each data point to get the exact info you're looking for, rather than typing in the search bar over and over again.
It's one of my favorite sites. Let me know if this helps!
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