Acknowledge each version, with the required wording.
Most Bible publishers freely offer permission to quote from their copyrighted translations. There’s no need to fill out formal requests or to pay a fee—if your use meets certain conditions and you give proper credit.
Most publishers set similar guidelines for how much of their translation you can cite, as well as how they want it acknowledged. Here’s what Crossway says about using their English Standard Version (https://www.crossway.org/permissions/):
The ESV text may be quoted (in written or print form) up to and inclusive of five hundred (500) verses without express written permission of the publisher, providing that the verses quoted do not amount to more than one-half of any one book of the Bible nor do the verses quoted account for 25 percent or more of the total text of the work in which they are quoted.
You’re okay as long as your use:
1) Is no more than 500 verses.
2) Quotes less than half of any one book. (Be careful in citing 3 John!)
3) Is no more than one-fourth of your manuscript.
That blanket permission covers you only if you cite the copyrighted translation on your book’s copyright page. Here’s the required language for using the ESV as your primary translation:
Scripture quotations are from the ESV® Bible (The Holy Bible, English Standard Version®), copyright © 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.
If you cite several Bible translation, but chiefly use one, you must credit each—identifying the one that’s primary. Here’s the terminology required for the NIV:
All Scripture quotations, unless otherwise indicated, are taken from the Holy Bible, New International Version®, NIV®. Copyright ©1973, 1978, 1984, 2011 by Biblica, Inc.™ Used by permission of Zondervan. All rights reserved worldwide. www.zondervan.com The “NIV” and “New International Version” are trademarks registered in the United States Patent and Trademark Office by Biblica, Inc.™
If you signal “all Scripture quotations, unless otherwise noted,” you needn’t put (NIV) after each quotation.
After giving permission credit for your primary translation, follow suit for all others you quote. The permission line is the same, except for the opening line:
Scripture quotations marked (NIV) are taken from the Holy Bible, New International Version® …
Public Domain Bibles
While most versions of Scripture are protected by copyright, a few are in the public domain, including these on BibleGateway.com:
American Standard Version (ASV)
Darby Translation (DARBY)
Douay-Rheims 1899 American Edition (DRA)
King James Version (KJV)
World English Bible (WEB)
Young’s Literal Translation (YLT)
Reina-Valera Antigua (RVA)
Biblia Sacra Vulgata (VULGATE)
You can find online each version’s official permissions language. If the version is among the many on BibleGateway.com, visit their available versions list, click on the translation’s name, such as the Holman Christian Standard Bible, then select the link for its copyright information.
Otherwise, enter a phrase such as “Bible Version Permission Statement” into a search engine. You’ll quickly find the copyright holder’s policy for what you can cite and how to give credit on your book’s copyright page.