This article proposes a novel two-staged trajectory planning algorithm toward the cooperative visual coverage of multiple asteroid sites with the utilization of multiple spacecraft. The objective of the novel established planning scheme is to determine an observation tour for each spacecraft and the associated fuel optimal trajectories, such that each site of interest is observed only once during the entire mission. The completion of the observation task of an asteroid site is limited to the observation time window, referred as the period for which a site is illuminated by the Sun. The proposed planning algorithm divides the overall multi-site coverage problem into a nonlinear and integer optimization problem as: (i) a single target optimization and (ii) a multi-target multiple spacecraft optimal sequencing problem. The first part aims to generate fuel optimal trajectories, for all the initial-final imaging site location pairs. In the second part, the problem of distributing the observation task, among the fleet of spacecraft, is addressed by designing a feasible tour to observe a subset of the desired asteroid sites, for each spacecraft, while considering their individual fuel capacity. The efficacy of the proposed algorithm is evaluated in multiple simulation scenarios and while considering different asteroids.