Can my Darius, Trifarian become active state if I first play a card first, then play Darius?

Yes. If Darius is your second card played this turn, he readies himself and gets +2 Might.

A card is "played" when it fully resolves. Darius enters the board as part of his resolution, so he's already on the board when the "when you play your second card" trigger checks — he sees himself as that second card and triggers. The first card you played before him is what made him the second (FAQ #1119, #4088).

Note: if he's played as the 3rd card or later, he won't trigger — the condition has already passed and he can't count future cards after himself.