We investigate low-temperature spin correlations in the metallic frustrated magnet β-Mn1-xCox. Single-crystal polarized-neutron scattering experiments reveal the persistence of highly structured magnetic diffuse scattering and the absence of periodic magnetic order to T=0.05 K. We employ reverse Monte Carlo refinements and mean-field theory calculations to construct an effective Hamiltonian which accounts for the magnetic scattering. The interactions we identify describe an emergent spin structure which mimics the triangular lattice antiferromagnet, one of the canonical models of frustrated magnetism.