Can I get a cocaine possession charge expunged from my record?

Depends.  Each state has its own set of requirements for expungements.  For instance, capital felonies, 1st degree felonies, violent felonies, sex offenses, etc., cannot be expunged. Plus, you cannot have picked up any additional charges.

Moreover, all fines must be paid in full and the time period for from the date of conviction has elapsed.

Consult with a local attorney or google your states criminal code regarding expungements and see if you qualify.

Hope this helps