If you are talking about reading/parsing JSON objects, than you can use Gson library witch is a part of Hadoop distribution on Dataproc.
Also, you can use JSON library of your choice and any other dependencies, but you should create uber jar for your job and include all these libraries/dependencies into it.
If you are talking about Google JSON API Client libraries, than Dataproc by default deploys 1.20.0 version as part of GCS and BQ connectors. You still can use newer JSON API Client library version if you will relocate it inside your job's uber jar to avoid conflicts with version deployed to Dataproc.
See more detailed answer on conflicting dependencies management in Dataproc here.