Okay. Here's from the 2nd edition of the OED:

"Inerrancy" was first used by Thomas Horne in his And Introduction to the critical study and knowledge of the Scriptures, 7th ed., which was published by T. Cadell in London.

"Inerrability" was first used in 1627 in Baiting Pope's Bull.

"Inerrable" was first used in Jackson's Creed in 1613.

The word does not have an origin in US, but in Britain. If you disagree, please talk to the folks at the Oxford English Dictionary.