Aim for the middle of any opening, which will automatically put you in the best position to avoid the hammers. If you spend too much time focusing on the hammers, you're almost sure to hit one well before you might like. Pay them as little conscious attention as possible.
Two Fingers Help
Playing with two fingers helps. Find a control setup that works for you, and apply it consistently so you don't have to stop and wonder which direction a tap will take the bird. If one finger regularly moves you left and the other regularly moves you right, that's two fewer things you have to think about and you should have an easier time falling into "the zone."