Hi Christina,
The NASPP has a full curriculum of courses that I recommend--this probably goes without saying but I'm saying it anyway ;)
For administrators at private companies, I recommend our "Equity Compensation Fundamentals - Private Companies" course. It would give you a broader understanding of equity plans at private companies, beyond just stock options and transaction processing.
If you feel you are beyond the fundamentals level, we have a number of more advanced programs that look at either specific awards types or specific aspects of plan administration (such as tax withholding and reporting).
In terms of certifications, I recommend the Certified Equity Professional program, which is specifically for equity plan professionals. It is a self-study program offered by the Silicon Valley Executive Center of Santa Clara University (the exams are administered remotely, so you don't need to travel to Santa Clara). That is the only certification program for equity plan professionals.