Here's my playlist from the program I put to air on 4 August 1996, with each song mentioning another month:

The Bold Poachers, Steeleye Span "Concerning of three young men/One night in January"
The L & N Don't Stop Here Any More, Michelle Schocked "And his face as white as February snow"
The Housewife's Lament, Anne Hills & Cindy Mangsen "In March it is mud"
And the Band Played Waltzing Matilda, Eric Bogle "So now every April I sit on me porch"
Mrs. McGrath, Pete Seeger "For a cannonball on the 5th of May"
Kilkelly, Moloney Keane O'Connell "Are going to get married in June"
Star of the County Down, Declan Affley "One morning last July"
Cyprus Brig, Margaret Walters "Twas August 1829, with 31 on board"
Heights of Alma, Liz & John Munro "The glorious 20th of September"
Mary Ellen Carter, Stan Rogers "She went down last October"
The Nightingale, Alan Scott "On the 14th of November last"
Currency Lasses, Gordon McIntyre & Kate Delaney "To sit in the stocks in the month of December"