Step 1: Write the complex ions involved.
Tris(ethylenediamine)cobalt(III) chloride contains the complex ion \([\mathrm{Co(en)_3}]^{3+}\), which is positively charged.
Potassium trioxalato aluminate(III) contains the complex ion \([\mathrm{Al(C_2O_4)_3}]^{3-}\).
Tetracarbonyl nickel(0) is a neutral complex \(\mathrm{Ni(CO)_4}\).
Diammine silver(I) chloride contains the complex ion \([\mathrm{Ag(NH_3)_2}]^{+}\).
Step 2: Identify the net charge.
Among the given options, only \([\mathrm{Al(C_2O_4)_3}]^{3-}\) carries a net negative charge.
Step 3: Conclusion.
Hence, potassium trioxalato aluminate(III) has a negatively charged complex ion.