1. can you talk with that individual professor to have your grade changed from C- to C. i do not think s/he will have much problem.
royi karai garera try that. if you can do that all your problem will be solved.
is s/he that tough to approach?

is this a core course in which you have C-?

2. your program director is also a real khadoos.. what else can i say. Program Director, or Dean has the discretionary power to actually override and let you slide if they want. Explain the situation to them. most of the time they help.

read your university course of studies that specifically outlines that the requirement for passing or graduation. is the requirement only GPA above 3. or does it also specify that you have to have grades above C in each courses or only core course.
this varies by university/colleges. you might just get lucky and slide by if nothing regarding grade is mentioned anywhere.
surprising that they have a fix at C. for graduate studies anything under B is almost worthless. you cannot transfer or anything so "C" or "C-" not a big difference. [ except pulling the GPA down]

No offense [ it would be nice to know the name of this school which has a big thing for C ]