One way to find these faithless damsels is to do a DT or DT/Forum search using "@a infidelity" or some such.
Among others, the DT has:
How could I forget?   The quintessential song of a faithless wife/lover, perhaps --
Blackjack Davey
The Raggle Taggle Gypsies
WHEN CARNAL FIRST CAME TO ARKANSAS
and some versions of The Gypsy Rover or The Whistling Gypsy.
 

The DT also has:
  Ballad Of The Waterfall
The Week Before Easter
Once I Had A Sweetheart
THE TRAIL TO MEXICO
ZULEIKA
PRETTY NANCY OF YARMOUTH
THE PLAIN GOLDEN BAND
THERE IS A TAVERN IN THE TOWN
SUSANNAH CLARGY
A SONG ON THE NANTUCKET LADIES
St. Louis Woman
New River Train
SALLY WHEATLEY
Once I Knew a Pretty Girl (The Rejected Lover)
PEGGY AND THE SOLDIER
MOUNT AND GO
CUCKOLDS All A-ROW
THE BUNCH OF VIOLETS
BOTTOMLESS WELL   (Shel Silverstein)
THE BROWN AND THE YELLOW ALE
BLACK-EYED MARY
Seven Nights Drunk
THE DOG IN THE CLOSET
THE BARLEY AND THE RYE
CHRISTINE LEROY
CARMEN
AS I WENT OUT FOR A RAMBLE
ANNIE BREEN
THE DOCKYARD GATE
DT search:  @infidelity