I have shipped and received several long guns (muzzleloaders) in well-packaged cardboard boxes. However, two years ago, I shipped two longrifles at the same time, I thought very well packed. One arrived broken. Badly broken. It was insured. To make a long story short, Fed Ex paid me a lowball price for a really nice rifle. It was time-consuming, a major pain, and a financial loss.
I received a Hawken fullstock from John Bergmann since then, and he shipped it in a wooden crate filled with foam, for a cutout for the rifle. It arrived in perfect shape. John understandably wanted his crate back, so I returned it, but building one of those from 1 x 4 (I think... might have been a little wider) for the ends and sides, and 1/4" or 3/8" plywood for top and bottom, would be easy for anyone with basic carpentry skills. I'm not sure where to get the foam, but I expect JoAnn's might have it. If I ship another long gun, I will build a crate like that for it.
*The first thing I would recommend is to watch Bob McBride's video (see post #8).
*Take multiple photos of your rifle before you pack it.
*Insure it for a realistic amount. If you spend the money for $10,000 worth of insurance for a $1,500 rifle, you're still not going to get more than the rifle is worth, and you'll probably get less, as I did.
*Do a search on this forum for threads related to shipping guns. The topic of shipping was covered fairly extensively, just recently.
Good luck! Like I said, I have sent and received a number of guns that were packed with newspaper in cardboard, and they got through fine, but I learned the hard way that you sure can't count on it. Be a pessimist. Plan for the worst.
Notchy Bob