J.C.
Your child, not his. It's not a tiny problem. As the child of a single mom myself, I know that I am totally biased, but the best gift my mother ever gave me was to be my mom first and foremost and being someone else's girlfriend was a lot lower priority.
Any amount of harsh is too harsh for a two-year-old, although you don't describe what you mean by that. I am NOT saying your boyfriend is inappropriate, but it's not his place to be disciplining his girlfriend's child. He's not a stepdad. Unless he's adopting, I don't think he should be deciding discipline.
If you do decide this is a long-term commitment, I highly recommend you both take a parenting class. My husband and I went to a STEP parenting class that our first son's preschool offered and it was really helpful in explaining developmental levels, common issues young kids have, and how to work with their understanding.
I want to add one last thing, and I hope it doesn't offend. But the statistics are a little scary. Any single mother needs to be cautious and to watch what's going on with the partner/child relationship.
http://www.msnbc.msn.com/id/21838575
"Children living in households with unrelated adults are nearly 50 times as likely to die of inflicted injuries as children living with two biological parents, according to a study of Missouri data published in the journal of the American Academy of Pediatrics in 2005."