Alexandrian tradition -
Coptic Catholics: (non-voting) Patriarch Emeritus Antonios Cardinal Naguib.
Byzantine tradition -
Italo-Albanese Catholics: Apostolic Administrator Paolo Cardinal Romeo
Romanian Catholics: (non-voting) Lucian Mureşan, Cardinal, Major Archbishop
Chaldean tradition:
Syro-Malabar Catholics: George Alencherry, Cardinal, Major Archbishop
Antiochian tradition:
Maronite Catholics: Béchara Boutros Raï, O.M.M., Cardinal, Patriarch
(non-voting) Nasrallah Pierre Cardinal Sfeir, Patriarch Emeritus
Syro-Malankara Catholics: Baselios Cleemis (Isaac) Thottunkal, Cardinal, Major Archbishop
Armenian tradition:
Armenian Catholics: No current cardinals.
Non-voting cardinals are any cardinals over the age limit of 80.
A lot of Eastern groups are apparently up for new cardinals soon, or are between bishops or patriarchs for various reasons. I haven’t listed which churches have had cardinals in the past and don’t have them now, or which churches have never yet had cardinals. So there are many rites not listed above.