When I don't have an egg tray or egg carton how to carry eggs without breaking them?
One of the old classic methods used sawdust (dry sand also works): put a layer of sawdust in a (wood) box, nest some eggs into it (well separated from either other and the side/bottom of the box). Add more sawdust, until you can nest another layer of eggs with similar separation between layers as between eggs in a layer. Continue until you run out of eggs or space.
Another method (which also helps preserve freshness without refrigeration) is to pour barely-melted bacon fat (or plain lard) over the eggs, which are nested into a container like a bucket. The fat prevents movement, which would be required for the eggs to break; it also excludes air, reducing the speed of spoilage.
You could use a tube (like the core roll from aluminum foil, which is about the right size) -- plug the tube with something soft and resilient, like high density foam, add an egg, another plug, etc.
What all of these methods have in common is that they immobilize the eggs, as well as preventing external impact. Anything that accomplishes both ought to work.