I am a fellow cat fanatic with a similar goal to yours, though I have realized it is not practical to finish off my photo list which is similar to yours (though I have black-footed cat from a few places in USA and I have melanistic pampas cat from years ago at Cincinnati Zoo).
@Chlidonias provides an excellent list. I will post my list but most of it duplicates his. I will go in order from most common to least.
Also if you have not been to Le Parc Des Felins in France you need to go. It is unbelievable and my favorite zoo.
Black-Footed Cat. There are several in USA zoos, including San Diego Safari Park, Fresno Chaffee Zoo (though Asia construction may have removed them), Utah Hogle Zoo, Riverbanks Zoo, etc.
Pampas Cat. Bioparque M'Bopicua (Uruguay), Sao Paolo Zoo (Brazil), and off exhibit at Santiago Zoo and Buin Zoo (Chile).
Flat-Headed Cat. Khao Kheow Open Zoo and Chiang Mai Zoo (Thailand).
Kodkod (aka guigna). Off exhibit at Santiago Zoo and Buin Zoo and a private collection (Chile).
Marbled Cat. Taiping Zoo Night Safari (Malaysia), Sitesh Babu Zoo (Bangladesh), and off exhibit at Al Bustan Zoological Centre (UAE). See this thread:
Marbled Cats in Zoos
Sunda Clouded Leopard. Formerly at Lok Kawi Wildlife Park (Malaysia, but likely now died), Taman Safari Bogor (and also Prigen according to Chlidonias) (Indonesia).
African Golden Cat. Private rescue center (Gabon). A former ZooChatter who worked in the zoo industry once stated there were a pair held privately in South Africa but he was unwilling to give any details.
Bornean Bay Cat. None currently, but one was recently exhibited for a brief period (before it died) at Taman Safari Bogor (Indonesia).
Andean Cat. None currently (or ever as far as I know), but a rescued cat was held briefly off exhibit for rehabilitation at Vesty Pakos Zoo (Bolivia). See this photo in the gallery:
Andean cat! March 2016 - ZooChat