Let me answer this for acyclic quivers, if there are cycles it should be the same, but to be on the safe side let me not claim it in that generality.

The path algebra is hereditary (i.e. of global dimension 1), from which it follows that the Hochschild cohomology vanishes above the global dimension. Hence $\operatorname{HH}^2(A,M)=0$.

If there are relations, the global dimension jump ups.