For UPS, you must take the firearm to one of their hubs (the Customer Counter, specifically, its the place where all their trucks originate from for your area) or, if you have a UPS driver come by your house or business every day (a Daily Pickup Account, you have to pay for that service), you can hand it to the driver with a prepaid label.
It will cost you like $40 to overnight a handgun (handguns must go at least Next Day Air Saver).
Kharn