How do I go about balancing these equations?
I agree with you, the right equilibration of the redox reaction is the following:
$$\ce{4 Co^2+(aq) + 2H2SO3(aq) + 2H^+ (aq)-&gt; 4 Co^3+(aq) + S2O3^2- (aq) + 3H2O(l)}$$

The problem is  in your assumptions about the oxidization number change at the beginning, and more precisely about sulfur.
The oxidation number of  sulfur in $\ce{H2SO3}$ is four. But in thiosulfate ion, you have two inequivalent sulfur atoms: 
Please see:
 Oxidation states of the sulfur atoms in the thiosulfate ion
The oxidation number is $\ce{+IV}$ for the central one, while it's zero for the terminal one.

In sum, the variation in the oxidation number for sulfure is four, not two.
(As if you have two sulfur atoms with oxidation number of four in $\ce{2H2SO3}$. One of them changes its oxidation number to zero. while the other one stays intact).