Is there a verb or adverb to describe the overly friendly speech or tone of someone who has said something bad about you behind your back but doesn't know that you know?
You may be best served by a nice descriptive adjective in this case. Here are a couple that fit:
too sweet or sentimental : sweet or sentimental in a way that does not seem sincere or genuine
Source: Definition of “saccharine” at merriam-webster.com
causing or tending to cause disgust or aversion through excess:
a perfume of cloying sweetness.
overly ingratiating or sentimental.
Either can be made into adverbs in the usual way (by adding “-ly”), the latter more comfortably than the former (though “cloyingly” should probably always have “sweet” tacked onto it in use).
ingratiating - "intended to gain approval or favor; sycophantic"
Also, bamboo's "two-faced" is spot on.