Construction grade silicon or perhaps some type of Loctite. We use it plenty on brick when we are not allowed to drill.
Love it when a customer insists on no drilling.....blockheads (pun intended).
Like Pat said, the silicone will make more of a mess than drilling a few holes. If the sign is ever removed, you will never notice the holes (plus they are easy to patch, if so desired). If customer says no holes....I say, Get someone else to install.