My daughter was born in 2009, I know who her father is but I did not have his name put on the birth certificate because he had expressed no interest in acting as a father. In fact, previously he had always said if I got pregnant he would want me to get an abortion. I refused to consider that so now I am a single mother. Is there any possible way for her father to force me to allow him to see her? (I live in Michigan and he is currently in North Carolina)

Sure its possible. All he needs to do is go to court and excersize his rights to the child.

A father has equal rights to any child they have. Just because you left him off the birth certificate (which might have been illegal) doesn't mean he loses those rights.

All he needs to do is go to court to enforce his rights. This will mean a paternity test to establish that his is the father, but once that's done he will be declared the legal father. As the legal father he might even be able to get primary custody, though that is a long shot. Unless you can prove he is a danger to the child, there is little reason he will not be able to get visitation. On the other hand, you can file for child support from him.

Yes, he can easily get visit rights, merely apply to the courts, get a DNA test done. Depending on the terms he may be forced to do a parenting class, start with supervised visits, but he will easily get visits unless he can be proved to be a threat to the child.