Have you looked at the OSLC workshop? There you can quickly see how to get to the artifact types defined for a project or component, looking at the creation factory for a service provider. And yes you could use the private API, but usage at your own risk.

For completeness, the DNG public API's that are available are:
RRC Reportable API - creating custom reports to be run from DNG or RPE, read only.
OSLC RM V2 API - the open standard way to programmatically integrate with DOORS Next Generation, there is an elaborate workshop to get you started; here the OSLC Workshop article. These programs can be from any language that support HTTP REST calls, e.g. Java, C# etc. Hence these are more flexible to run and can read and update DNG data, as part of a web server, or standalone, but have some limitations set by the current OSLC standard, for example module support. In release 6.0.5 extension have been added for modules.
DNG Server API's - starting with version 6.x, various public RM server API's have been added, also REST API's, for configuration management, task tracker, modules, ReqIF, and type import.
TRS 2.0 - the OSLC Tracked Resource Set open standard REST API to hook into the stream of low level changes done to resources in the DNG application (and other Jazz apps as well); read only.
Client extension capability - these are Javascript extension that are added as widgets you can run from the dashboard, and can be used to view and edit DNG data. It's more tailored to DNG, so has better module support, but is limited to run in a browser/javascript environment.

And as I mentioned above, there is the private REST API, which you could reverse engineer looking at the requests/responses, but it isn't documented and supported, and can change over time, so usage at your own risk.