Are finite-domain binary constraint satisfaction problems solvable in polynomial time?
I don't know, but if you manage, make sure to let us know. 

The reduction seems easy indeed, with $d$ mapping to the number of colors and each constraint to an edge.

However, a polynomial-time algorithm for any $\mathcal{NP}$-complete problem exists if and only if $\mathcal{P} =\mathcal{NP}$; doing what you ask would imply $\mathcal{P} \neq \mathcal{NP}$.