If I play two Darius on my turn, do I ready both Darius due to its ability?

Yes, both copies of Darius will trigger and ready themselves.

According to the RiftJudge FAQ (ID 8029): "Ruling: Both Darius cards trigger. When the second Darius is played, he sees himself as the second card played that turn."

Sequence of events:

1. Play Darius #1: He enters the board.
2. Play Darius #2: He enters the board.
3. Trigger: Because Darius #2 is the second card played this turn, both Darius #1 (already on the board) and Darius #2 (having just entered) meet the condition of "When you play your second card in a turn."
4. Resolution: Both abilities are placed on the chain (Rule 376.3). Since you control both, you choose the order in which they resolve (Rule 376.3.b). Both will gain +2 Might and become ready.