Assume $(\mathbb{P}$ is c.c.c.$)^M$ and $\Diamond$ holds in $M[G]$. Show that $\Diamond$ holds in $M$.
Hint: It is sufficient to verify $\Diamond^-$ in $M$.
Should I try to create a $\Diamond$ sequence or $\Diamond^{-}$ sequence? Should I work with nice names?
If $\langle A_\alpha:\alpha<\omega_1\rangle$ is a $\diamondsuit$-sequence in $M[G]$, pick $p\in G$ such that $$p\Vdash \langle \dot A_\alpha:\alpha<\omega_1\rangle\text{ is a }\diamondsuit\text{-sequence}.$$ Now consider, in $M$, for each $\alpha<\omega_1$, $\mathcal A_\alpha:=\{A\subseteq\alpha:$for some $q\leq p, q\Vdash \check A=\dot A_\alpha\},$ then each $\mathcal A_\alpha$ is countable.