We present a path planning algorithm for time-critical cooperative surveillance using a set of unmanned aerial platforms. The unique constraints imposed by maneuver limits and body-fixed cameras make the problem quite challenging. An Integer Programming (IP) based strategy for successfully operating within these constraints is developed. The main contribution of the paper is the incorporation of highly constrained motion and sensor capabilities of the vehicles in the mathematical programming formalism. Simulation and experimental results are presented to demonstrate the efficacy of the proposed approach.