If you haven't read it, check out my previous article about Using Jersey 2.x as a shared library on WebLogic 12.1.2. If you're not using WebLogic 12.1.2 or Jersey as a shared library, this article is still relevant but you'll have to take care of your own service packaging.
First add Jackson as a dependency to your Maven POM.
Then in your application class (the one that extends ResourceConfig) make sure to register the JacksonFeature class. If you're not familiar with the Jersey application model, read about it here.
Finally in your resource (the class annotated with @Path, as described here) add @Produces annotation with MediaType.APPLICATION_JSON as the parameter. This tells Jersey that your resource will produce JSON output. The annotation can be either on the resource class itself, or any of the methods that are required to produce JSON output.
All you then have to do is add a return type to your resource method. In my particular case I used a Map
The output generated becomes something like this:
As you notice there is no code to manually convert my Map