I tried to put a spawner inside a container to spawn stealable, and I want to make it only spawn when a player with a certain quest item comes in range. I set the triggeroncarried, however, it doesnt get triggered. I made an exact same copy of the spawner and placed outside container, it triggers.

This makes me wonder somehow proximity trigger for something inside a container is not working properly, since it doesn't have light of sight? Just a blunt guess, any help would be appreciated!

you could have it spawn the item inside the container. this doesn't require the spawner to be inside the container.
this might help
How Do I - Add items to a spawned mob or container

As far as i know, you can't. Since the contents of a container is not located on the same place as the container.

What you can do instead is to place the spawner outside the container, and use the SETONNEARBY attribute. For more info on this attribute, check out the "nearbyboxes.xml" spawn file, located in the Spawns folder. Or you can check out some threads about it on this forum. Like the following one...

http://xmlspawner.15.forumer.com/index.php?showtopic=850

Hope this helps.

Yes that helped! Thank you!