What preposition to use with "enamour"?

Solution 1:

The distinction isn't as great with the British spelling (enamoured) NGram using the British spelling of enamoured, which may be what prompted the OP's question.

I actually hear more people say "enamored by," which is incorrect. I think this is a funny and memorable explanation of the preposition to use with enamored:

Enamored By ( or ) Enamored Of:

If you’re crazy about ferrets, you’re enamored of them.

It is less common but still acceptable to say "enamored with."

But if you say you are enamored by ferrets, you’re saying that ferrets are crazy about you.

Solution 2:

"Enamoured of" is the most common, according to Google NGram: