Yes – there is a setting that will defer all student detentions until the day after they are earned. This means that any student who earns a detention today will not show up on the "To Serve Today" detention roster until the next day.
Find the "Served Tomorrow" settings in the "Detention" category on the Settings page (you may need the proper permissions to access this page – contact your Schoolrunner administrator for assistance). There are unique settings for after-school detentions and lunch detentions.
Note that this setting serves a different function from detention snoozes. Detention snoozes are used to delay specific student detentions to a future day that may be further in the future than tomorrow. This setting will defer all student detentions only to tomorrow.