I found this solution on the Magento forum, so all credit goes to the original poster. I added it here to make it easier to find.
The Magento database makes use of foreign key constraints to ensure database integrity. As an example, if a category is deleted, all categories below it in the category tree must be deleted too.
If you make a backup of your Magento database using the built-in backup function (Admin > System > Tools > Backup), Magento inserts special statements in the .sql file to avoid foreign key checks when the tables are restored.
If you backup your Magento database using other tools, like phpMyAdmin or Navicat, these special statements will be missing. When you attempt to run the .sql file, you will get errors like these:
Cannot add or update a child row: a foreign key constraint fails
This error occurs because the data you are importing is provided table by table, row by row, without regard to the logical structure and integrity of the database.
To restore a .sql file backup without constraint checking, simply add the following statements at the beginning of your .sql file:
SET NAMES utf8;
SET @OLD_UNIQUE_CHECKS=@@UNIQUE_CHECKS, UNIQUE_CHECKS=0;
SET @OLD_FOREIGN_KEY_CHECKS=@@FOREIGN_KEY_CHECKS, FOREIGN_KEY_CHECKS=0;
SET @OLD_SQL_MODE=@@SQL_MODE, SQL_MODE=’NO_AUTO_VALUE_ON_ZERO’;
SET @OLD_SQL_NOTES=@@SQL_NOTES, SQL_NOTES=0;
At the end of the file, add the statements required to turn on constraint checking again:
With these modifications, you should be able to restore your Magento database from a .sql file backup created with any tool.
Hope this helps.