You cooperate with God...
...just not in the very act of conversion. But after your conversion and rebirth in Holy Baptism you do cooperate with God. Here is another great quotation from Gerhard's Theological Commonplaces, On Free Choice. This volume will be ready sometime in 2013, I think.
(IV) [Bellarmine again:] “God works in us to will by helping and exciting [us] so that we in truth do the willing. Yet this does not occur without us, otherwise the apostle would not say: ‘Work out your salvation with fear and trembling’” (Philippians 2).
We respond. The apostle is speaking about the reborn who can cooperate after their regeneration through the new powers given by God. But the question here involves the act of conversion itself, that is, what can the human will accomplish in that act of itself and of its own natural powers? This certainly does not yet amount to cooperation but only passivity [παθητική].