First: If it was the majority of the day or night, then that might be considered as a day or a night, but if it is just a snippet at the end or beginning, then hardly could that be considered as such.
Second: The three days and three nights has to be fulfilled. Using the "part = a whole" argument, the shortest the three day period could be is: part of a day + a full night + a full day + a full night + a full day + part of a night. That means that He had to be buried atleast by Thursday. Friday won't work.
Third: Jesus was not buried until after evening on Passover. Joseph of Arimathea did not even go to Pilate until evening [sunset] had come. That rules out one of your three days needed in your accounting.
Finally: The Passover Crucifixion was in 30 AD and Passover in 30 AD was a Wednesday not a Friday.
Well, Jesus died at 3:00 in the afternoon. There is still a large portion of the day left.
If the 3 days and 3 nights, as postulated by the Church and many others, actually means, as shown numerous times throughout the Bible, as on the third day - as it also says in the three other Gospels - then Friday does work.
And are you really sure that Jesus really did die in 30 AD?