Loc: Royse City, TX
USPS will not take my guns if they know it's a firearm. Or at least they wouldn't the last couple times I tried probably 5-6 years ago. Neither would fedex, but UPS would if you knew which one to go to.
Loc: Virginia, USA
I ship my firearms to outfitters all the time.... I use FEDEX 3 day ground. I have never had an issue. As long as you are not selling the firearm I do not think you have an issue either. Also, consider that you need to ship a firearm to a manufacturer for a recall and they use carriers.