Strongest conjugate base is

If acid is weak, its conjugate base will be strong. Greater the oxidation number of Cl, stronger the acid and thus, weaker the conjugate base.
$$\begin{gathered} \underset{+1}{\mathrm{HClO}},\underset{+3}{{\mathrm{HClO}}_2},\underset{+5}{{\mathrm{HClO}}_{3^{\mathrm{\prime }}}}\underset{+7}{{\mathrm{HClO}}_4} \\ \to \end{gathered}$$
Oxidation number of Cl and acidic strength increases.
$$\begin{gathered} {\mathrm{ClO}}^{-},{\mathrm{ClO}}_2^{-},{\mathrm{ClO}}_3^{-},{\mathrm{ClO}}_4^{-} \\ \leftarrow \end{gathered}$$
Conjugate base strength increases.
Hence, CIO^- is the strongest base.