Daily Clan Challenges start at 5pm every weekday (UK time) and end the following day at 4pm.
Obviously if your looking for US times, it's 8 hours earlier.
In case your still struggling with Elite,
Monday: Most wins in any game mode
Tuesday: Most Captures in Capture the Flag Core mode
Wednesday: Most Captures in Domination Core mode
Thursday: Most defend in Capture the Flag Corw mode
Friday: Most kills in TDM core mode
Saturday: Clan Ops - Kill Confirmed, Most confirmed kills.
Sunday: Clan Ops - TDM, Most Kills.