Finding skyrmions in different kinds of structures has attracted a lot of attention but also remains a challenge. Here we study the adsorption of transition metal atoms (Cr, Mn, Fe, and Co) deposited on top of a monolayer MoS₂ where the transition metal atoms form a triangular lattice. First-principles DFT calculations suggest that the magnetic ordering of this triangular lattice corresponds to a 120-degree antiferromagnetic structure. Heisenberg exchange parameters, single-ion anisotropy constants, and Dzyaloshinskii-Moriya vectors are extracted by choosing different spin configurations and calculating the total energy differences. For the considered transition metal atoms, the ground states are found to be spin spirals formed from 120-degree antiferromagnetic states. Our study shows the potential to find skyrmions in such triangular lattices.