Can BB gun be sent through UPS?

Yes. Under US law, a BB gun is not a firearm. They may be shipped by common carriers, such as UPS.

But they cannot be sent through the U.S. Mail. According to the Domestic Mail Manual - Firearm means any device, including a starter gun, designed to, or that may readily be converted to, expel a projectile by the action of an explosion, spring, or other mechanical action, or air or gas pressure with enough force to be used as a weapon.