= Solution
Since $CJ_3C^{-1}=-J_3$, the operator $C$ sends a weight-$m$ state to a weight-$-m$ state. Also
$$
CJ_-C^{-1}=-(J_1+iJ_2)=-J_+.
$$
For the spin-one normalization,
$$
|1,0\rangle=\frac1{\sqrt2}J_-|1,1\rangle,
\qquad
|1,-1\rangle=\frac1{\sqrt2}J_-|1,0\rangle.
$$
Write $C|1,1\rangle=a|1,-1\rangle$. Using $C|1,0\rangle=|1,0\rangle$ in the first relation gives $a=-1$, and applying $C$ to the second gives the other phase. Therefore, in the stated phase convention,
$$
C|\pi^+\rangle=-|\pi^-\rangle,
\qquad
C|\pi^-\rangle=-|\pi^+\rangle.
$$
A simultaneous phase redefinition of the charged pion states changes both displayed signs but not their physical interchange under <charge conjugation>.
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