What is the oxidation number of carbon in the ion (Co3)2-?

The oxidation number of the carbon is +4.

Oxygen normally has an oxidation state of -2.

Oxygen = three ions each with a charge of -2 = 3 x -2 = -6 The overall charge of the polyatomic ion is -2

This means that the oxidation number of the carbon must be +4.

Total charge = +4 + -6 = -2

Here is a video which discusses this topic by discussing how to determine of in the bicarbonate and dichromate ions. Video from: Noel Pauller

Hope this helps!