An easy option is to add the data folders for the container you are using as a volume mapped to a local folder. Then the container will just put the files there and you can backup the folder. Restore is just put the files back there, then make sure you set the same volume mapping so the container already sees them.

You can also use the same method to access the db directory for the migration. Typically for databases you want to make sure the container is stopped before doing anything with those files.