How to convert joda dateTime to string in swagger

I am not sure how to add your custom converters to swagger 1.5. But these are workarounds for your use case:

You can create a Model and replace it in the generated swagger object, before converting it to Json.

ModelImpl m = new ModelImpl()
          .description("LocalDateTime in ISO format")
          .format("ISO DateTime")
          .name("DateTime")
          .type("string");
Response response = getListingJsonResponse(app, context, sc, headers, uriInfo);
Swagger swagger = (Swagger) response.getEntity();
swagger.getDefinitions().put("LocalDateTime", m);

That will replace the definition of LocalDateTime with a string type model.

The other way will be to iterate through the definitions, and wherever you see the reference type to LocalDateTime, replace that with a string type:

Map<String, Model> definitions = swagger.getDefinitions();
  for(Map.Entry<String, Model> e : definitions.entrySet()){
    Map<String, Property> propertyMap = e.getValue().getProperties();
    for(String key : propertyMap.keySet()){
      Property value = propertyMap.get(key);
      if(value.getType().equals("ref") && ((RefProperty) value).getSimpleRef().equals("LocalDateTime")){
        propertyMap.put(key, new StringProperty("LocalDateTime in ISO format")
                .example("dd-mm-yyyy")
                .pattern("pattern")
                .description("ISO format string"));
      }
    }
  }

As of now I am unaware of any other cleaner way to achieve this.

UPDATE

Swagger has a mapping for DateTime and not LocalDateTime. So you can also consider moving your types to DateTime if that works for you.