It is shown that, for the von Neumann algebra $A$ obtained from a principal measured groupoid $\mathcal{R}$ with the diagonal subalgebra $D$ of $A$, there exists a natural ‘bijective’ correspondence between coactions on $A$ that fix $D$ pointwise and Borel 1-cocycles on $\mathcal{R}$. As an application of this result, we classify a certain type of coactions on approximately finite-dimensional type II factors up to cocycle conjugacy. By using our characterization of coactions mentioned above, we are also able to generalize to some extent those results of Zimmer concerning 1-cocycles on ergodic equivalence relations into compact groups.