In the olden days, AA and other airlines use to give out cardboard boxes to pax with not too durable looking or exotic luggage to check which was not, in the checkin agent's view, sufficiently durable. Or just on request. These were specially made, printed with the AA logo and had a big folding handle on top. I checked my backpack with dangling straps in many of these in years gone by.

Somehow, I doubt they are still giving these away.

But, any strong box should do. Remember the fifty pound limit.