Me too had similar problems on a PLL synthesizer board,
and in my case were the piezolelectric behaviour of
some SMD capacitors. I really proved this phenomenon
desoldering the capacitors and fixing them on a small
piece of PCB then excitating it with a vibrating tip.
An oscilloscope connected to the capacitors under test
showed the waveform of the vibration as a few millivolts
peak to peak signal.
Since these caps was located in the loop amplifier/filter, the
disturbing signal was amplified and FM modulated the VCO
(which was suspended by means of rubber strips)
I reduced the microphonic effects of at least 20dB mounting
in place of the SMD caps some traditional caps of the same value.
Note that, in my case, the phenomenon was present only in
high valued (47-100nF) caps. Other caps ranging from 4.7 pF to
4.7nF seemed to be immune.
Lastly, remeber that also coil inductors are microphonic and, when
possible, it is convenient to block their windings with some glue or
use a piece of short circuited semirigid cable in place of them.
Hoping this could help.