We investigate spin-polarized electronic structures of CoX$_2$ (X=S, Se, Te) monolayers using the density functional theory. We find that CoS$_2$ and CoSe$_2$ monolayers are metallic ferromagnetic materials, whereas CoTe$_2$ monolayer is non-magnetic metallic material. The 3D bulk layered crystalline structures of CoX$_2$ (X=S, Se, Te) are found to be non-magnetic metals in our calculations. In addition to the major contributions due to the $d$ orbitals of Co atoms, there is also contribution from the $p$ orbitals of chalcogen X atoms to the magnetism in CoX$_2$. The crystal field spliting and distance between the neighbouring magnetic atoms play a significant role to induce magnetism in these structures. We are optimistic for the experimental growth and uses of these monolayer structures for the 2D spintronic applications.