Deformations of dihedral representations

G. Burde proved (1990) that the $\mathrm {SU}_2 (\Bbb {C})$ representation space of two-bridge knot groups is one-dimensional. The same holds for all torus knot groups. The aim of this note is to prove the following:
Given a knot $\k \subset S^3$ we denote by $\Hat C_2$ its twofold branched covering space. Assume that there is a prime number $p$ such that $H_1(\Hat C_2,\Bbb {Z}_p)\cong \ZZ_p$. Then there exist representations of the knot group onto the binary dihedral group $D_p \subset \mathrm {SU}_2 (\Bbb {C})$ and these representations are smooth points on a one-dimensional curve of representations into $\mathrm {SU}_2 (\Bbb {C})$.