Prudently; circumspectly; cautiously; judiciously; with nice judgment of what is best to be done or omitted.

adverb. Acting in a discreet manner; one that respects privacy or secrecy; quietly; diplomatically.

adverb. Inconspicuously.

adverb. with discretion; prudently and with wise self-restraint

"Forbidden from evangelizing, American Christians who teach English or work in social service agencies in China spread the word discreetly."

Wheatley  completely  neatly  sweetly  

artfully  astutely  cannily  carefully  cautiously