The correct answer to this open question is the following.
No, it could not.
Although the states of New Hampshire and New York ask the Confederate Congress to solve the problem, the central government under the Articles could not resolve this issue because, under the Articles of Confederation, the central government was weak and had little power to make decisions like this. Under the Articles of Confederation, it was the states the ones that were sovereign and could collect money through taxation. The central government -Congress- had to ask for money from the states in case Congress needed it. Congress had few unimportant powers such as to rule the operation of the post office.
That is why many delegates met at the Constitutional Convention held in the city of Philadelphia, Pennsylvania in the summer of 1787, to debate on the new form of a central government for the United States and the creation of a new Constitution.