Hey Sheila,
You can just call me Joe

Im sure you have heard of Belfast's many troubles over the years, it has never been the most peaceful of cities. Im from West Belfast. The city is kinda 'ghettoised' as West Belfast is mainly Catholic, North and South mixed (where you may find most trouble happening) and the East is mainly Protestant. Your grandfather as you have stated was Catholic? That would make it more unusual for him to have come from the mainly Protestant East Belfast, but i myself have an aunt who moved there, and my grandparents on my father's side (That is the Ward family name side) lived fro a short period in East Belfast as in those days it was much more peaceful and less likely to cause tension. Im not sure what the demographics would have been in those days regarding the proportions of what faith, people followed in those areas but my guess is it would be relatively similar to today as it takes very long for things to change around here.
My Granda Ward he is called William Ward, i just noticed someone mentioned a William Ward further back, hmm well he was only born in 1934, but im unsure of what his father would have been called, i will check with my dad when he gets back. Hmm your father said something about him being from St Peter's Parish? well there is St Peter's Cathedral in West Belfast.....just wondering could the East Belfast thing be wrong? Just its more likely for a Catholic to be from West Belfast than East....though as i said its far from impossible. Im not as au fait with my family history as i should be, i have trouble enough remembering birthdays

All i'm really going on is the area similarity and the coincidence of our families names (which so far has been slightly uncanny i suppose, as familys usually pass down names right?) I hope im being of some help and not just leading you down blind alleys.
Joe