According to this link, their stamps changed in 1961. I cant find out that they changed to....
These are the independence set of stamps issued by Kenya in 1963. Kenya was independent for a full year before becoming a republic. None of these 1963 stamps say republic. Someone has earlier posted a 1964 stamp that says Republic on it, but it could have been issued in december 1964 when it was a republic. I will post only two 1963 stamps and a link for people to see many more of them to avoid cluttering up the thread with too many images.
see: http://kenya-stamps.bonnyrigg.net/kenya/ken-sg1-14.htm