You should invite whoever you want to invite, and if that means inviting everyone in her class except Darius, so be it. The thing is, you need to make it a party where you are inviting her friends as opposed to inviting her class. If it so happens that her friends are everyone in her class except Darius, well, that's just the way it worked out. You do this by mailing invitation to their homes, rather than passing them out in class. Passing them out in class makes is a pseudo-school related event and it would be rude to exclude anyone. By mailing the invites you are taking the "classmate" element out of it and making it about friends.
What your daughter needs to know if that she cannot then say to Darius, "I'm having a party and you can't come! Nyah!" Sure, other kids will talk about it, but that's them. That's got nothing to do with your daughter; she can't control their actions. If Darius asks her why he can't come, you can teach her to say something like, "I'm just having my friends over for my party." This would be a good opportunity for him to learn cause and effect...as in, if you are mean to someone, you don't get invited to their parties.
If his parents ask you about it, I would say something along the same lines. "Oh, sorry but we're only inviting her friends to this party." If they push the issue then I think it's fine to say "She would be uncomfortable having him at her party because he picks on her and calls her names."
I don't think there would be anything rude about that.