  We consider deformations of a group of circle diffeomorphisms with H\"older
continuous derivatives in the framework of quasiconformal Teichm\"uller theory
and show certain rigidity under conjugation by symmetric homeomorphisms of the
circle. As an application, we give a condition for such a diffeomorphism group
to be conjugate to a M\"obius group by a diffeomorphism of the same regularity.
The strategy is to find a fixed point of the group which acts isometrically on
the integrable Teichm\"uller space with the Weil-Petersson metric.
