I am going to use Amex from now on, nowI have read this thread. I hadn't thought Amex was an option as the logo wasn't advertised.
Until now I have always had to use a visa broker when travelling through Kenya. There are loads online if you Google it and they are quick. Looks like I used ivisa.com last time. These visa brokers have their payment systems set up. The problem is they charge like twice the price of what the visa should cost if you buy it directly from the governmental site.
Kenya really should sort this out. I actively avoid Nairobi as a hub because of the visa issue. At least with the Amex trick the visa costs are not too bad now.