UPS provides Saturday delivery for time-critical shipments. (I'm currently not aware of any Sunday delivery) The times they will commit to depend on the service you choose. Here is what they stated as of 2009.
UPS Next Day Air® Early A.M.®: Guaranteed delivery one hour later than the guaranteed weekday delivery time, as early as 9:00 a.m., based on estination UPS Next Day Air®: Guaranteed delivery by 12:00 noon or 1:30 p.m. where weekday shipments are delivered by 10:30 a.m. or 12:00 noon, respectively, based on destination UPS 2nd Day Air®: Guaranteed delivery by end of day for shipments picked up on Thursday, based on destination UPS Worldwide ExpressSM Plus: Delivery based on destination UPS Worldwide ExpressSM: Delivery based on destination
In the United States, UPS will pickup on Saturday in every state except Hawaii if you schedule it with them here - Saturday pickup. If you have a critical need, UPS Express Critical® is available 24/7 – even on holidays. 1-800-714-8779. There is no regular Sunday pickup.
UPS does not delivery on Saturday or Sunday. Business days are Monday through Friday. So if you place an order for next-day delivery and it leaves our warehouse on Friday, it will be delivered on Monday, the next business day.