I just checked my copy of the King James version, and it has no copyright notice.
I've no idea what the copyright laws are in respect to Bible translations.
Well, the bible itself obviously can't be copyrighted, as it's been around for ages. The king james version is very old, and a copyright term for most things in the US is the life of the author plus 70 years. So, you simply take the author's death date, add 70 years, and the work will not be protected after that date.
However, a translation is a fair amount of work and involves both incorporating the original work and adding substantial modifications. In this respect, a translation's "author" is not one person, but a group of people.
We should also note that anyone can claim copyright on anything they write Whether that holds up in court is another matter.