We consider a distributed detection system for a wireless sensor network over slow-fading channels. Each sensor only has knowledge of quantized channel state information (CSI) which is received from the fusion center via a limited feedback channel. We then consider transmit power allocation at each sensor inorder to maximize a J-divergence based detection metric subject to a total and individual transmit power constraints. Our aim is to jointly design the quantization regions of all sensors CSI and the corresponding power allocations. A locally optimum solution is obtained by applying the generalized Lloyd algorithm (GLA). To overcome the high computational complexity of the GLA, we then propose a low-complexity nearoptimal scheme which performs very close to its GLA based counterpart. This enables us to explicitly formulate the problem and to find the unique solution despite the non-convexity of the optimization problem. An asymptotic analysis is also provided when the number of feedback bits becomes large. Numerical results illustrate that only a small amount of feedback is needed to achieve a detection performance close to the full CSI case.