Mission Aviation Fellowship (noted above) is about the only organization I know of that utilizes 'volunteer' pilots. They are a respectable organization with very high standards, however, it is a prerequsite that you are an active 'Christian' with a capital C - I believe that the various volunteers (pilots, engineers, etc.) are also expected to organize funding from their local church congregation in their home country to cover travel costs, living expenses, etc. That's not meant to be a criticism of the organization, it's just the way it is.
Outside of MAF, I'm not aware of any aviation operations in Africa that use 'volunteers', regardless of how great their experience may be. Normally, humanitarian and non-governmental organizations who need aircraft for development, disaster relief, or war relief activities contract out their aircraft requirements to local businesses. This model is followed worldwide.