The Church announced back in 2011 that there would shortly be a new API available to download church published content including scriptures and other manuals.
This release did not happen. There has been significant discussions internally, but no new announcements. No further information is available.
This wiki page will be updated if/when there is news to share. Feel free to signin here and add this page to your watch list.
More information about the use of Church copyrighted material can be found in the Rights and Use Information linked at the bottom of the page.