  We present a comprehensive single crystal neutron diffraction investigation
of the $\rm Mn_{1-x}Co_{x}WO_4$ with $0.02\leq x \leq0.30$. At lower
concentration $x \leq 0.05$, the system is quickly driven into the multiferroic
phase with spin structure forming an elliptical spiral order similar to the
parent compound. The reduction of electric polarization is ascribed to the
tilting of the spiral plane. For $x\sim 0.075$, the magnetic structure
undergoes a spin flop transition that is characterized by a sudden rotation of
the spin helix envelope into the $ac$ plane. This spin structure persists for
concentration up to $x=0.15$, where additional competing magnetic orders appear
at low temperature. For $0.17 \leq x \leq 0.30$, the system experiences another
spin flop transition and recovers the low-$x$ spiral spin configuration. A
simple commensurate spin structure with $\vec{q}=(0.5,0,0)$ is found to coexist
with the incommensurate spiral order. The complex evolution of magnetic
structure in Co doped $\rm MnWO_4$ contrasts sharply with other transition
metal ion doped $\rm Mn_{1-x}A_xWO_4$ (A=Zn, Mg, Fe) where the chemical
substitutions stabilize only one type of magnetic structure. The rich phase
diagram of $\rm Mn_{1-x}Co_{x}WO_4 $ results from the interplay between
magnetic frustration and spin anisotropy of the Co ions.
