Let's say that humanity somehow has colonized almost every celestial body in the solar system (with the exception of the gas giants, Venus and Mercury): we mine moons and asteroids, we live on planets, etc. There now exists a problem in keeping humanity united; the calendar. The Gregorian calendar used on Earth in no way slides nicely into the cycles of other bodies. The highest point in the solar empire has decided that a new calendar should be put into place and has hired the system's greatest minds to design it.
What would this new calendar look like? What would need to be done so that all the dates, day, week, month and year, all coincide with each other? Keep in mind that the calendar must be able to be read and understood in every area of the solar system.