Probably 3 pm on Thursday, April 6, AD 30.
Using modern techniques, astronomers are now able to work backwards to determine dates. Using key time-stamped passages in the Bible, they've determined that Jesus died in the spring of either 30 or 33 AD. My personal opinion is that most likely Jesus died at 3 pm on Thursday, April 6, AD 30 as explained below.
A "Sabbath Day" was a day of rest. The Hebrew word "Sabbath" is derived from the Hebrew word for "rest". In most cases, this was every Saturday of the year. But at the time of Passover, there were two extra days of rest (or Sabbaths).
Ex 12:15 “‘Seven days you shall eat unleavened bread; even the first day you shall put away yeast out of your houses, for whoever eats leavened bread from the first day until the seventh day, that soul shall be cut off from Israel. 12:16 In the first day there shall be to you a holy convocation, and in the seventh day a holy convocation; no kind of work shall be done in them, except that which every man must eat, that only may be done by you.
As these Sabbaths could be any day of the week, they were also called "special" Sabbaths. Most people, when attempting to determine when Jesus died, overlook or ignore those special Sabbaths.
Jn 19:31 Therefore the Jews, because it was the Preparation Day, so that the bodies wouldn’t remain on the cross on the Sabbath (for that Sabbath was a special one), asked of Pilate that their legs might be broken, and that they might be taken away.
Tracing back the Jewish lunar calendar, Bible scholars have calculated that the first day of the Unleavened Bread Feast was on a Friday, April 7, AD 30. Therefore that would have been a day of imposed rest (i.e. a Sabbath). That obviously meant that Jesus died the day before, Thursday about 3 pm, which gave Nicodemus and Joseph of Arimathea about three hours to bury Jesus' body before sundown when the special Sabbath began.
Interestingly, the Greek word (Sabbaton) in Mt 28:1 often translated as “Sabbath” is actually a plural form of the word, hence some translations (ISV, YLT) translate the word as “Sabbaths”, thus it was after the “Sabbaths” that Mary Magdalene came to the tomb.
Therefore Jesus was buried for three days and three nights just as he predicted (Mt 12:40), although the first "day" was a very short one, possibly only minutes.
(Also note that “three days and three nights” was somewhat of a Hebrew idiom and did not literally mean always three full days and nights, i.e. 72 hours, but could include parts of a day or night.)
I think it was in the fourth century that some people decided rather than go with a specific date for Easter, they would follow the Jewish Lunar Calendar instead, where exact dates can fluctuate.