I am preparing an AR upper for shipment.  Do I need to write anything special on the box?

Fragile and Do Not Drop would be my suggestion.  I really don't know if you have to write anything special.

No special markings,
Just pack it very well and tape it well.  Try to use a new or new looking box.  And If you want the cheapest rates use the website [www.ups.com] to make your own account which you can pay by CC (I use my Check Card).  That way you don't have to tell anyone what's inside the box.  After you print out your own label with the 1Z shipping number you can attach it to the box and give the package to any driver or drop it off at any shipping place (Mail Boxe Etc, Parcel Plus, Office Depot) for pick-up.  I usually print two of the labels and put one in the box incase the one outside the box gets ripped off in the equipment or gets wet and illegible.

The only thing that has to go Next Day Air is handguns, you can ship your rifle Ground.  I would insure it for what you think it would cost to replace, it's automatically insured for $100.00  Insurance isn't that much so definately do it.  In your best interest you can also make it 'Singature Required', or 'Adult Signature Required' when you print your own label, it'll cost a couple of dollars extra but then the driver cannot driver release the package, he would have to have someone sign for it.

BTW, I'm a UPS Driver