We investigate the Josephson coupling of two conventional superconductors with phase difference φ through a diffusive contact made of two ferromagnetic domains with a noncollinear orientation of the magnetization vectors with an angle θ. Using the quantum circuit theory, we find that in addition to the charge supercurrent an spin supercurrent with a spin polarization normal to the magnetization vectors will flow through the contact. While the charge supercurrent is odd in φ and even in θ, the spin supercurrent is even in φ and odd in θ. We also predict a transition between 0 and π Josephson couplings with varying θ. Furthermore, for the low exchange fields, by inserting asymmetric insulating barriers at the interfaces of the system with φ = π, the domains prefer antiparallel configuration. We show that the situation reverses when the exchange field increases. Also, we find the domains in the symmetric systems always comfort in a parallel configuration when φ = π. Finally, we discuss the spin supercurrent in an extended domain structure with multiple domainwalls.