What can I do if my collaborator is enthusiastic, but their PhD student is not? I am collaborating with a professor (and thus one of his PhD students). The professor likes me and my idea, but the same cannot be said about the PhD student. 

The PhD student takes much longer than he normally would to do simple tasks which are essential for the project, and regularly points out flaws in the research design. Every research has its limitations, and I agree those are limitations, but I don't agree that they are nearly as severe as they are made out to be.

If interpreted generously, the PhD student is less enthusiastic about the project. If interpreted harshly, the PhD student is actually trying to sabotage the project.

Obviously I only want to complain to the professor as a last resort. What can I do to make the PhD student more enthusiastic?
Instead of "making" the student do or be anything--which is impossible anyway--you could try treating the student as a junior collaborator rather than a gopher. Or maybe the student simply doesn't want to do this project at all. 

Some people are passive-aggressive because of personality issues, but in the case where there is an enormous power disparity, many people are passive-aggressive because they don't have any other way of expressing their unhappiness about something. So it's up to you (or the advisor) to broach the subject.

You could take the point of view that the student should do whatever we want and shut up about it, but pragmatically, this approach hasn't been working out so well, so maybe it's time to try something else.