Some time ago, I came across a web page characterizing a dictionary of Kenzi Nubian dating from 1635 as "the oldest dictionary of an African language". Much as I appreciate their work in getting this very interesting material online, that claim is out by at least 500 years, if not 1000.
The oldest arguable dictionary of an African language that I am aware of so far is the Greek-Coptic Glossary of Dioscorus of Aphrodito, which apparently* dates back to the 6th century. Ibn al-'Assal's Arabic-Coptic sullam muqaffa, written in the 1200s, can quite unhesitatingly be described as a dictionary; following a then-current Arabic tradition, it was arranged alphabetically from the last letter of the word backwards (so, for instance, "apple" would be close to "people" but far from "apricot".) This arrangement was meant to aid in the composition of rhymed prose and verse. Other examples, many arranged semantically, are given by the Encyclopedia of Islam article Sullam (literally "ladder"). In Ethiopia, traditional Geez-Amharic lexicons are titled Sawasew, or "ladders"; I thus assume they are of Coptic inspiration, though I haven't been able to find any detail about when they started to be written.
After Coptic, the next oldest is an Arabic-Berber lexicon written in 1145, containing some two thousand words. Its writer, Abu Abdallah Muhammad ibn Ja'far al-Qaysi, better known as Ibn Tunart, was born in Qalaat Bani Hammad (modern Algeria) and wrote the work in Fez (Morocco) - a second little-known Algerian medieval linguist to add to my list after Ibn Quraysh! The book contains some paradigms and verbs, but consists principally of a list of Arabic nouns with Berber equivalents or glosses, arranged by semantic field; it inspired several later Moroccan lexica. Nico van den Boogert is working on republishing it.
What other African dictionaries predate Carradori's? I don't know, but I can hazard some guesses - Geez, Swahili, Kanuri, and Nubian itself would certainly be worth checking.
* According to Adel Y. Sidarus, “Coptic Lexicography in the Middle Age, The Coptic Arabic Scalae,” in The Future of Coptic Studies ed. R. McL. Wilson (Leiden: E.J. Brill, 1978), 123
28 minutes ago