  In this paper, we study special cycles on the Kr\"amer model of
$\mathrm{U}(1,1)(F/F_0)$-Rapoport-Zink spaces where $F/F_0$ is a ramified
quadratic extension of $p$-adic number fields with the assumption that the
$2$-dimensional hermitian space of special quasi-homomorphisms is anisotropic.
We write down the decomposition of these special cycles and prove a version of
Kudla-Rapoport conjecture in this case. We then apply the local results to
compute the intersection numbers of special cycles on unitary Shimura curves
and relate these intersection numbers to Fourier coefficients of central
derivatives of certain Eisenstein series.
