String result = objectMapper.writeValueAsString(map) - as simple as this!
Result:
{"2019-07-04T03:00":1,"2019-07-04T04:00":1,"2019-07-04T01:00":1,"2019-07-04T02:00":1,"2019-07-04T13:00":1,"2019-07-04T06:00":1 ...}
P.S. add Jackson JSON to your classpath.