Enamored of/with/by

Solution 1:

Looking at Google Ngrams, British English seems to use nearly exclusively "enamoured of", while American English uses both "enamored of" and "enamored with". "Enamo(u)red by" is quite rare on both sides of the pond. I would probably say "enamored of" when talking about a person, an animal, or an abstract idea, and "enamored with" when talking about a tangible object. I can't tell whether this is just me, or American usage in general. After looking at some examples on Google, I can say lots of people don't follow this rule.

He was enamored with his new model airplane.

He was enamored of the idea of running his own business.

But all three of these prepositions are acceptable grammar, and all three should be understood equally well.

Solution 2:

Instances of enamoured of overwhelmingly outnumber the other two in the Corpus of Contemporary English, the British National Corpus and the Oxford English Dictionary. All three seem to be more common in British English than in American English.

Hey, I see you're at Brigham Young. You can get corpus data from their site right here.

Solution 3:

I found this answer here: http://public.wsu.edu/~brians/errors/enamored.html

"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."