My daughter and her boyfriend have been living together approximately 2 years. They have a child together. He is the owner of the house. Can he evict her?

Yes, She has no rights to live in the house other than the rights of any tenant. If he no longer wants her there, he can evict her as long as he does it legally. On the other hand, she can get custody of the child and force him to pay support.

An “eviction” is a legal proceeding. And if he doesn't want her to stay anymore with her, he can evict her easily as she has no rights of any of the tenant.
But she can get custody (Custody of a child) and explain him the best interests of the child standard.

Unless her name is on the house, or unless she has a written lease, and because they are not married, yes, he can evict her.

If things are that bad, she should file for custody of child and child support