there is a song from an old cartoon that goes
"I was walking thru the park one day
in the merry, merry month of may
when i was taken by surprise
by a pair of (roving?) eyes....


but the best song that has May in it is
the Soldier and the Lady, or the fiddling soldier,
the bold grenadier, the brave volunteer,
a.k.a. One Morning in May...as first heard from
James Taylor (possibly learned from Jim Rooney)

http://www.mudcat.org/thread.cfm?threadid=3646

it starts : One morning, one morning, one morning in May,
I spied a young couple; they were making their way...

and the chorus goes:
Just to see the waters gliding and hear the nightingale

sing.