I'm not aware that hotels allow you to purchase 1/2 days.
Some hotels offer early check-in or day-use for less than the price of an overnight stay.
Some hotels will let you go to your room as soon as it's available - Not the usual practice in Japan but more likely at a non-Japanese deluxe property where you have status.
Some will keep you waiting until exactly check-in time, when a long queue will snake its way to the front desks. Visit the dingy lobby of the Prince Hotel in Shinagawa one afternoont to see this miserable spectacle play out.