I've had similar problem. And a linux admin here in my office showed me how to use SUDO.
I'm still learning in the Linux world (on CentOS actually) so I'm not sure if SUDO is used for all Linux flavours.
Basically you setup your system to use sudo and give different rights for each users. Following link is my quick list reference for sudo related questions, I'm sure there are better sites around and even here... http://itg.chem.indiana.edu/inc/wiki/software/165.html
Note also that if you are personally using root as your main access you should really consider using sudo for yourself as well.
Once you have sudo setup and your users configured to use it he/she will be able to use the command :
sudo asterisk -rx 'sip reload'