The rapid proliferation of unmanned aerial vehicle (UAV) applications imposes stringent requirements on continuous and reliable communication coverage in low-altitude airspace. Conventional cellular systems built upon fixed-position antennas (FPAs) are inherently constrained by static array geometries and limited mechanical degrees of freedom, which severely restrict their ability to adapt to highly dynamic three-dimensional (3D) propagation environments. Movable antenna (MA) technology has recently emerged as a promising paradigm to overcome these limitations by actively reconfiguring electromagnetic radiation characteristics through controllable antenna positioning and array orientation, thereby enabling flexible spatial coverage adaptation. To systematically quantify the airspace coverage capability of MA-enabled systems, this paper formulates a spatial coverage maximization problem over a discretized 3D voxel space. For each voxel, the received signal-to-noise ratio (SNR) is maximized via joint optimization of the MA's 3D positions and beamforming matrices. To efficiently solve the resulting non-convex problem, a hybrid particle swarm optimization and simulated annealing framework is developed to search for high-quality antenna configurations. Simulation results demonstrate that the proposed MA design framework substantially outperforms conventional FPA-based schemes in terms of spatial coverage, achieving coverage rates of 26.8% and 29.65% for airspace below 300m and 600m, respectively. Moreover, further coverage enhancement can be attained by incorporating mechanical tilt adjustment, highlighting the strong potential of MA technology for reliable low-altitude communication coverage.