The Bachelors
the casuals
I think he sang "Bitches Get Stiches" And then I'm 100% sure he sang "Scream For My Ice-Cream"
Brothers Four-1960
Dahvie Vanity and Garrett Ecstasy i think
John Lennon, George Harrison, Paul McCartney and Ringo Starr.
The Trashmen - in 1963. See related link to Youtube.
Mary Hopkin (sang Those Were The Days in the 1960s)
"Mony Mony" was a hit for Tommy James & the Shondells in 1968.
The only song with that title to ever chart in the US was by Perry Como in 1971
sounds like a grass roots song.
I believe you are thinking of Lynne Randell, an Australian singer who was very popular for a brief time in the mid-1960s, and even went on tour with the Monkees. "Ciao Baby" was a hit for her in 1967.