Dana Lyons wrote and recorded JUNE IS A COMING, available at https://youtu.be/1ez1DOKchD0

Lots of months get mentioned in this song, set in Seattle. The first stanza goes,

The Fall is the sunniest time of the year
And the mountains are clear every day,
But November it brings home the clouds
And the rain once again,
December is many warm nights by the fire
Reading stories and sipping some beer,
With the days growing longer,
The end of the winter seems near.

The 2nd stanza mentions March. We finally get to June in the 3rd stanza:

June is a coming, the salmon are running
And I've got to be on my way,
I don't want to leave you my darling
But there's so many more debts to pay,
They say that the catch will be bigger this year
And we'll all come home rich in the end,
I don't want to leave you my darling,
But the nets will be loaded by dawn,
June is a coming and I must be rolling along.