I think we can get 1 or 2 bets depending on the player but always starting on the turn. What is his range for calling twice preflop? Pretty wide, but we can probably discount AK (which he would likely ship given 2 opportunities).
I agree we can check the flop. There are a number of bad turns for us. AJQ9 and any club (to a lesser extent). This is quite a few cards to dodge BUT he has a clear check-shoving range of combo draws on this board which will force us to give up a decent amount of equity.
So the turn we can bet after he has checked for a 2nd time. Occasionally he has a passive Kx but he can also call with everything that might have shipped the flop and also he should have a lot of pocket pairs and some Tx.
River is player dependant. We are getting closer to the situation where he only calls with better. Safe option is check back. If you have seen him make calling errors then bet ahead and hope to see a pocket pair, Tx, or 7x

. Feel like getting creative? Since we think he can have every big draw that we didn't let shove over us on the flop maybe this could be a nice spot to bet 1/4 pot to try and induce a bluff shove