Tanzanians never say "no" to anything. They will never tell you that anything is not possible. Even a "yes" can simply mean "maybe." A Tanzanian saying often used in lieu of a straight "no" is "inshallah" (god willing), which seems to be an African favorite in general.
Inshallah can mean anything from "this situation is really out of my control at this point, but I have done everything I can do to make it happen - and inshallah, it will" to "despite the fact that it is completely in my power to solve your problem, I have done nothing at all to help you, but god willing someone else will - or possibly God will grace you with a miracle and get it done so that you won't ask me again."
If s/he says nothing, smiles, and shakes his or her head "yes," then just pack up and go home. Whatever it is, it is definitely not happening and s/he hopes that you will leave soon so that s/he can stop smiling.