The most un-rhyming (probably made that up) song I know is The Galway races:
As I roved out to Galway Town to seek for recreation On the seventeenth of August my mind was elevated There were multitudes assembled with their tickets at the station And my eyes began to dazzle and they're going to see the races
Chorus With a wack fol the do fol the diddley didle aye
There were passengers from Limerick and passengers from Nenagh Passengers from Dublin, sportsmen from Tipperary There were passengers from Kerry all the quarters of the nation And our member Mr. Hasset for to join the Galway Blazers
There were multitudes from Aran and members from New Quay shore The boys from Connemara and the Clare unmarried maidens There were people from Cork City who were loyal, true and faithful That brought home Fenian prisoners from dying in foreign nations
It's there you'll see confectioners with sugarsticks and dainties The lozenges and oranges, the lemonade and raisins The gingerbread and spices to accommodate the ladies And a big crubeen for threepence to be picking while your able
It's there you'll see the gamblers the thimbles and the garters And the sporting Wheel of Fortune with the four and twenty quarters There were others without scruple pelting wattles at poor Maggy And her father well contented and he looking at his daughter
It's there you'll see the pipers and the fiddlers competing The nimble footed dancers and they dancing on the daisies There were others crying "cigars and lights and bills for all the races With the colours of the jockeys and the prizes and horses' ages
It's there you'll see the jockeys and they mounted up most stately The pink and blue the red and green the emblem of our nation When the bell was rung for starting all the horses seemed impatient I thought they never stood on ground their speed was so amazing
There was half a million people there of all denominations The Catholic, the Protestant, the Jew, the Presbyterian Yet there was no animosity no matter what persuasion But joy and hospitality inducing fresh acquaintance
Garters and quarters are the closest, otherwise nothing. Made it a difficult song to learn by heart.