As mentioned in the excellent answer by janoside, you need to construct the JSON string and set it as a StringEntity
.
To construct the JSON string, you can use any library or method you are comfortable with. Jackson library is one easy example:
import com.fasterxml.jackson.databind.ObjectMapper;
import com.fasterxml.jackson.databind.node.ObjectNode;
import org.apache.http.entity.ContentType;
import org.apache.http.entity.StringEntity;
ObjectMapper mapper = new ObjectMapper();
ObjectNode node = mapper.createObjectNode();
node.put("name", "value"); // repeat as needed
String JSON_STRING = node.toString();
postMethod.setEntity(new StringEntity(JSON_STRING, ContentType.APPLICATION_JSON));