The radome of an airliner is attached to the fuselage with a number of fixings, (four?). If each of these incorporated a strain gauge, then the dynamic pressure of the air on the radome as a consequence of the forward motion of the aircraft could be measured and converted to an airspeed. In theory, this system would be immune to icing and insects etc., since there would be no holes or pipes which are prone to blockage.
And/or you might be able to make a similar measurement on the slats, or the fin mountings.
I wonder if this would be accurate, sensitive and stable enough to give a useable IAS readout?