Actually you can do this now:

http://hostname:8080/job/jobname/promotion/latest/internal_release/api/xml

As long as you know the job and promotion names, you are good to go.

Deleted my comment...

That does work to get the promotion status, how do you get the config? For a job you can get:
http://hostname/job/jobName/config.xml
so I thought a promotion might be:
http://hostname/job/jobName/promotion/promotionName/config.xml
but that doesn't work.

One of my projects depends heavily on the jsonp interface (pure xhtml/javascript), using jenkins as backend engine.

I only discovered some promotion information accessible through json api: the latest promotion build number (not the build number of the job being promoted) from permalinks:
job/<jobname>/promotion/latest/<PromotionName>/api/json
and eventually information of every promoted build:
job/<jobname>/<JobBuildNumber>/promotion/<PromotionName>/promotionBuild/<PromotionBuildNumber>/api/json

But the response does not contain any information related to build number of the origin job being promoted, so I basically cannot tell which build has been promoted by which promotion build, which is exactly the information I want to get.

It would be nice if the following information could be exposed through remote access api:
a) promotion status for each build, and/or
b) a summary/history of all promotion builds with reference to the being promoted build number.

Was fixed in 2.12 but I guess the JIRA link daemon was down.