Rema patches and glue are available in bulk for very reasonable per-unit prices. For example, you can get the 100-pack patch and 8-oz bottle of rubber cement for about $24, making it $0.24 per patch. That 8-oz bottle can probably last 400 patches if you're at all careful so really, it's about $0.17 per patch over 400 patches. As I understand, inner tubes are really cheap in bulk (<US$1 each) but patches are cheaper still and you won't have to worry about getting the correct size(s).

Rubber cement and cutouts from old inner tubes, as toddbiker mentioned, is also workable. But you'll really need to clean those mating surfaces well to make a durable patch.

If the hole is very small, creating a device to pump water into the tubes will work. But I suspect water may be a precious enough resource in many parts of Tanzania that using it to refill tires may not be viable. Along the same lines, I've heard that one can try to stuff dry grass into the tire in lieu of the inner tube to make the bicycle rideable, but I've never done it myself.

Finally, if you're insistent on getting the bikes running again, try contacting bike-centric philanthropic groups like Tom Ritchey's Project Rwanda. Even if they cannot help you, they may know someone who can.