  We study the dynamical equilibrium correlation function of the
polaron-dressed tunneling operator in the dissipative two-state system. Unlike
the position operator, this coherence operator acts in the full
system-plus-reservoir space. We calculate the relevant modified influence
functional and present the exact formal expression for the coherence
correlations in the form of a series in the number of tunneling events. For an
Ohmic spectral density with the particular damping strength $K=1/2$, the series
is summed in analytic form for all times and for arbitrary values of
temperature and bias. Using a diagrammatic approach, we find the long-time
dynamics in the regime $K<1$. In general, the coherence correlations decay
algebraically as $t^{-2K}$ at T=0. This implies that the linear static
susceptibility diverges for $K\le 1/2$ as $T\to 0$, whereas it stays finite for
$K>1/2$ in this limit. The qualitative differences with respect to the
asymptotic behavior of the position correlations are explained.
