If this is a rainbow flop I feel fine checking back almost any turn and giving up on the hand. Even with the flush draw I thought it was pretty close. You mentioned that vs a flush draw "we're doing fine" but probably almost any flush draw here has two overs to our pair so they're basically flipping with us. So vs some chunk of his range (ace high) we're drawing to two outs and vs some chunk of his range (flush draws) we're about a flip. I think I just talked myself into wanting to check back the turn here regardless of flush vs nonflush flop. What do you think?
Edit: I mean yes there is money in the pot and we need to protect our equity in it but when this player type continues on this type of flop it's overwhelmingly an ace imo. Aren't there way more combos of Ax than of flush draws?
My intuition says it's a close bet on the turn. My stoving says it's an easy check. 
Board: 2d Ah 9d 4c
Dead:
equity win tie pots won pots tied
Hand 0: 13.223% 13.22% 00.00% 2688 0.00 { 66 }
Hand 1: 86.777% 86.78% 00.00% 17640 0.00 { ATs, A8s-A5s, A3s, KdQd, KdJd, KdTd, Kd9d, Kd8d, Kd7d, QdJd, QdTd, Qd9d, JdTd, Jd9d, Jd8d, Td9d, Td8d, 9d8d, 8d7d, AJo-ATo, A8o-A5o }
Really would have thought we had more equity, but i suppose the sheer number of Ax's is just far greater than flush draws. I like a check now.