Answer
The chemical formula for the conjugate acid of $S{O_4}^{2-}$ is:
$HS{O_4}^-$
Work Step by Step
To find the conjugate acid of a base, you just need to add a proton $(H^+)$ to the compound.
1. Add one hydrogen.
$S{O_4}^{2-} --\gt HS{O_4}^{2-}$
2. Add "+1" to the charge of the compound:
$-2 -- \gt -1$
$HS{O_4}^{2-} --\gt HS{O_4}^-$