UPDATE: This is wrong answer, but it's still useful to understand why it's wrong. See comments.
How about unicode-escape?
>>> d = {1: "ברי צקלה", 2: u"ברי צקלה"}
>>> json_str = json.dumps(d).decode('unicode-escape').encode('utf8')
>>> print json_str
{"1": "ברי צקלה", "2": "ברי צקלה"}