Yes, you can GRANT him privileges to that database without giving him the main CPanel password.
There are 2 things that need to be done:
A) Grant him a username/password and access to that database
B) Give him a PHPMyadmin installation that does not require the CPanel login.
The best way to do this is as follows:
1) Download PHPmyadmin from http://www.phpmyadmin.net
and install PHPMyadmin into some directory under his public_html (say public_html/pmy/
2) Login as root to your server, type: mysql
3) at the mysql> prompt, type:
GRANT ALL PRIVILEGES ON database_name.* TO firstname.lastname@example.org IDENTIFIED BY 'passw0rd3';
(where 22.214.171.124 is his IP mask, or you can enter somename@"%" to allow any IP.
4) After PHPMyadmin is unzipped into public_html/pmy/, edit the config file and enter his username and password you entered in the mysql command above
5) Point your browser to the website.com/pmy/ and login
I hope this has been of any help. If you wish, feel free to ask me to login to your server, I would gladly do this for you.