The answer varies depending on the mover you select. Most long distance movers offer services seven days a week, but not every company may be available on that day.
If the company provides a holiday to its employees on Sunday, you may not be able to book a moving slot during that day of the week. It is often the case with local movers that Sunday is not an option.
When moving during the week is not an option, it is wise to book your movers for Saturday.