I played for St Pat's (Grangetown) from the early 60's through to late '70's, a decade or more when the club dominated the Cardiff and District League. My recollection is that different challengers came along for maybe 2 or 3 years at a time and then faded out of the picture. Grange Albion, St Albans, St Mary's (Canton) were among the biggest rivals in that time but I'm sure there were others I've forgotten. The 'EYE' - based in Ely I think - were certainly around during those years and came through to the 'first' division towards the end of my time, most likely in the 70's I'd say.
I don't recall much about them but think they played in black & white quarters? And ask your dad if one of his pals would go by the nickname "shovel" who was a complete nutter