"enthusiasm with" is correct and can be used in written English.
For example, "I was filled with enthusiasm with my new project."
Musicians express similar enthusiasm, with less formality.
He chats with enthusiasm with whoever is around.
"Investors should temper their enthusiasm with common sense.
But Skinner greets my enthusiasm with a weary shrug.
Politics is enthusiasm with a collective; with love, two people.
His parting words for the week were laced with enthusiasm, with reflection, with insight.
Romney noted that Paul "ignites an enthusiasm with a number of people.
But the most encouraging result of all is the enthusiasm with which Pakistanis have endorsed democracy.
Italy's new economics minister combines childish enthusiasm with ambition, wariness, wide interests, chutzpah and humour.
More notable is the way he mixes wide-eyed enthusiasm with sombre, ambivalent notes.
The enthusiasm with which their shares were touted helped to feed past market booms and busts.
