Tikva, your sil is lovely.
Is that a knitted blanket she's using??
I don't know about the rest of Africa, but I remember at least one Ethiopian carrier which we saw displayed in a restaurant here in the States was very much similar to the mei-tai. Only made of animal hide and decorated with white shells. The shoulder straps were much shorter though, with loops at the end. It almost looked like the mother would tie the bottom straps, and then pull the top straps over her shoulders and actually hold them? Maybe? Dh remembers seeing babies carried in those. When we were in Ethiopia, we also saw babies tied onto their mother's backs in large blankets, or with the large white shawls the women wear.
Now, my dh, on the other hand, once used a padded market bag (a large woven fiber bag).
He was supposed to be transporting a baby from a medical clinic back to it's foster family, and didn't have the means or the knowledge to wrap the baby. In his defense, at the time he was young, single and had never cared for a baby before. He got arrested because someone pegged him as a human trafficker and the doctor had to go down to the jail to explain what he was doing with a baby not his own and why it was in a market bag.
That probably doesn't qualify as "traditional", though.