Is the language of all TMs *not* accepting a given string, Enumerable?
The classic technique of dovetailing can be used to show the complement of $L$, $\{\langle M\rangle : M\text{ is a TM that accept }010\}$ is recursively enumerable. Check this answer for details.

Since $L$ is not decidable as shown by Rice's theorem, $L$ cannot be recursively enumerable.



Exercise. Show that $\{\langle M\rangle : M\text{ is a TM that accept } 010\text{ and }101\}$ is not in RE.