I think there's reason to believe that it might be on a Sunday when the end of the world/Second Coming happens. I'm not saying that it will be on that day. It's just that it would seem so since Sunday is the Lord's day. However, Jesus said, "And unless those days had been shortened, no flesh should be saved: but for the sake of the elect those days shall be shortened." (Mt. 24:22) But Jesus didn't say shortened in relation to what specific date. So we can't be certain the time when he will return, unless it's just about to happen. Jesus said that just before his return the sign of the Cross would appear in the sky (Mt. 24:30). That's the time when people can know for sure that it is imminent. Jesus also said, "From the fig tree learn its lesson: as soon as its branch becomes tender and puts forth its leaves, you know that summer is near. So also, when you see all these things, you know that he is near, at the very gates." (Mt. 24:32-33) And in the book of Daniel it says, "But you, Daniel, shut up the words, and seal the book, until the time of the end. Many shall run to and fro, and knowledge shall increase." (Dan 12:4)