Yep. You can allow them access to your database. Simply open your cpanel and click on MySQL Database Management icon. In MySQL section you will see an option at the bottom named "access hosts". Add his IP over there and then give him IP of the server, database name, database username and database password.
Make sure that you ask him to provide IP address of his machine by visiting whatismyip.com. If he says that his ISP allocated dynamic IPs to his machine then put "%" ( without quotes ) in access hosts section of your cpanel control panel. If you need help in creating database and assigning username to the database then go through cpanel tutorials located at
http://www.eukhost.com/support/cpanel.php