We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn₅ with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H || [100], a single VL orientation is observed, while a 90° reorientation transition is found for H ||; [100]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Γ =2.0 ± 0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H || [001]. At high fields, above which the upper critical field (H_c2) becomes a first-order transition, an increased disordering of the VL is observed.