No, the standard way to serialize to JSON is to use an existing JSON serialization library. If you don't wish to do this, then you're going to have to write your own serialization methods.
If you want guidance on how to do this, I'd suggest examining the source of some of the available libraries.
EDIT: I'm not going to come out and say that writing your own serliazation methods is bad, but you must consider that if it's important to your application to use well-formed JSON, then you have to weigh the overhead of "one more dependency" against the possibility that your custom methods may one day encounter a failure case that you hadn't anticipated. Whether that risk is acceptable is your call.