Actually, some local Christian groups do have arbitration groups.
They deal with small-time civil disputes. Participation is completely voluntary. Their decisions are not legally binding in any way that resembles the state's authority -- they have no power to fine or garnish wages, for example -- but their decisions are contractually valid, like binding arbitration.
I would be curious to know whether the Canadian arrangement allows the sharia courts to directly fine or garnish wages in cases calling for such sanctions, or whether they have to turn to the power of the provincial courts to enforce those remedies.