Problem:

I have:

www.A.com

www.B.com

I want to sync only databases of these two websites and I don't want to change the files.

Before that please read:

http://www.drmiri.com/computer/web-design/65-copy-or-backup-your-joomla

Procedure:

1. You should use JoomlaPack for making a backup from your Joomla Database (not including files). So, you should make a sql file from your A database and save it into your computer.
2. Then you should go to cPanel > PhPMyAdmin and Drop all tables within B Database and import A.sql file from your computer.