Is it unusual for a collaborator to ask for funding for a very short project? I am working on a paper that requires a comparison method to be implemented. The method of choice is not in my discipline. I asked a collaborator, who is an expert in the area and with whom I have several papers published, if he could implement it. It is about a week worth of work, most likely less. Both the collaborator and his professor would get an authorship on the paper. 

His professor said that the project can be only done if I had funding for him. The collaborator is already funded through an external fellowship. The project does not require any purchases. Is this an unusual request?
Seems to me like that's their way of saying "no".  One week of work in exchange for authorship is a great deal -- and you'd give authorship to the professor, too, in exchange for nothing?  Why would the professor say no?  I'm guessing that the professor doesn't think your research will succeed, or get published, and therefore doesn't want to invest the time.

I'd recommend just working with the student in his "spare time".  I'm sure it's worth his time in exchange for authorship.