  We characterise quasidiagonality of the $C^*$-algebra of a cofinal $k$-graph
in terms of an algebraic condition involving the coordinate matrices of the
graph. This result covers all simple $k$-graph $C^*$-algebras. In the special
case of cofinal $2$-graphs we further prove that AF-embeddability,
quasidiagonality and stable finiteness of the $2$-graph algebra are all
equivalent.
