The unpaired electrons in $Ni{\left(CO\right)}_4$  are

In $\mathrm{Ni}{\left(\mathrm{CO}\right)}_4,$the oxidation state of Ni is zero. Electronic configuration of Ni is $\left[\mathrm{Ni}\right]3{\mathrm{d}}^{8}4{\mathrm{s}}^2$. In presence of strong ligand CO,  the paring of electrons take place and electronic configuration will be $\left[\mathrm{Ar}\right]3{\mathrm{d}}^{10}4{\mathrm{s}}^0.$  Hence unpaired electrons is zero.