Small body missions can significantly benefit from deploying small landing systems onto the surface of the visited object. Despite the potential benefit that they may bring, deployments of landers in small body environments may entail significant mission design challenges. This paper thus addresses the potential of ballistic landing opportunities in binary asteroid moons from a mission design perspective, particularly focusing on reliability aspects of the trajectories. Two binaries that were previously identified as target bodies in several missions/proposals, Didymos and 1996 FG3, are considered in this paper. The dynamics near them are modeled by means of the Circular Restricted Three Body Problem (CR3BP), which provides a reasonable representation of a standard binary system. Natural landing trajectories that allow both minimum-velocity local-vertical touchdown and deployment from a safe distance are investigated. Coefficient of restitution values are used as a design parameter to compute the first touchdown speeds that ensure sufficient reliability of landing trajectories. A simple reliability index, which is derived via uncertainty ellipsoid from covariance analysis, is introduced to create a global reliability map across the asteroid surfaces. Assuming 3σ deployment errors on the order of 90 m and 2 cm/s, the results show that ballistic landing operations are likely to be successful for larger binary moons if the deployments target near equatorial regions within longitude range 320 ^o –20°. It has also been shown that the deployments to smaller binary moons may require higher accuracy in navigation and deployment systems in their mothership, and/or closer deployment distances.