To convert your object in JSON with Jackson:

import com.fasterxml.jackson.databind.ObjectMapper; 
import com.fasterxml.jackson.databind.ObjectWriter; 

ObjectWriter ow = new ObjectMapper().writer().withDefaultPrettyPrinter();
String json = ow.writeValueAsString(object);

Using org.json library:

try {
     JSONObject jsonObject = new JSONObject("{\"phonetype\":\"N95\",\"cat\":\"WP\"}");
}catch (JSONException err){
     Log.d("Error", err.toString());
}

No need to go with GSON for this; Jackson can do either plain Maps/Lists:

ObjectMapper mapper = new ObjectMapper();
Map<String,Object> map = mapper.readValue(json, Map.class);

or more convenient JSON Tree:

JsonNode rootNode = mapper.readTree(json);

By the way, there is no reason why you could not actually create Java classes and do it (IMO) more conveniently:

public class Library {
  @JsonProperty("libraryname")
  public String name;

  @JsonProperty("mymusic")
  public List<Song> songs;
}
public class Song {
  @JsonProperty("Artist Name") public String artistName;
  @JsonProperty("Song Name") public String songName;
}

Library lib = mapper.readValue(jsonString, Library.class);

There is a built-in method to convert a JSONObject to a String. Why don't you use that:

JSONObject json = new JSONObject();

json.toString();

Why not use GeoTools to handle the input and output? Then your code becomes simply something like:

File inFile = new File("/home/ian/Data/states/states.shp");
File outFile = new File("/home/ian/Data/states/states.geojson");
if (outFile.exists()) {
  outFile.delete();
}
outFile.createNewFile();
// Read
DataStore inputDataStore = DataStoreFinder.getDataStore(
        Collections.singletonMap("url", URLs.fileToUrl(inFile)));

String inputTypeName = inputDataStore.getTypeNames()[0];
SimpleFeatureType inputType = inputDataStore.getSchema(inputTypeName);

FeatureSource<SimpleFeatureType, SimpleFeature>
        source = inputDataStore.getFeatureSource(inputTypeName);

FeatureCollection<SimpleFeatureType, SimpleFeature>
        inputFeatureCollection = source.getFeatures();

Map<String, Object> params = new HashMap<>();
params.put(GeoJSONDataStoreFactory.URLP.key, URLs.fileToUrl(outFile));
// Write
DataStore newDataStore = DataStoreFinder.getDataStore(params);

newDataStore.createSchema(inputType);
String typeName = newDataStore.getTypeNames()[0];

SimpleFeatureStore featureStore =
        (SimpleFeatureStore) newDataStore.getFeatureSource(typeName);

featureStore.addFeatures(inputFeatureCollection);
newDataStore.dispose();
inputDataStore.dispose();

}

If you don't want to export all the attributes of the shapefile features you need to modify newDataStore.createSchema(inputType); to use a new limited schema. This needs something like:

SimpleFeatureType outType = DataUtilities.createSubType(inputType, new String[] {"type","REFCAT"});
newDataStore.createSchema(outType);