OneBody is powered by another of my projects http://bible-api.com (https://github.com/seven1m/bible_api), which just needs a little bit of code to return verses from the Apocrypha. If there's interest, I'd be willing to make it happen or show someone where to get started!
Part of the trick is that verses are numbered differently, for example, the Psalms. And Catholic Bibles have more chapters in Daniel and I think Esther. An API that would allow people to match verses across the two types of Bibles would have to have some kind of durable primary key for each verse in addition to its nominal address.
I'm guessing you're an LDS? I've always wondered if the church will release an API of sorts.. It would be nice to use for apps and who knows what else. A lot of the URLs on lds.org are quite SES/nicely formatted already, e.g. https://www.lds.org/general-conference/1973/10/behold-thy-mo..., and if they just added the option to return it in a different data format like JSON that'd be neat. ;)
Unless something has changed in the last 3 years, which knowing the internal systems of the LDS Church it is highly unlikely anything has changed, there will not be a JSON feed for the Book of Mormon anytime soon. They store all of the scriptures in proprietary XML formats inside of a large XML data store called MarkLogic. Although they could transform them into JSON, I just don't see them making that a priority.
However, I will also note that the Book of Mormon itself is no longer under copyright. The footnotes, indexes and chapter summaries are copyright protected but the book itself is not. So, really, it wouldn't be particularly hard to make a Book of Mormon rest api.
