I recall "Bless Me Father", set just after the war, but it was set in England.
Ballykissangel also has a young priest arriving in a small village set in Ireland, but it was set in the present (i.e. the time it was made, late 90s as I recall).
Then, of course, there's Father Ted...
Thanks. I see full episodes are available on You Tube. I especially liked the one where the little girl went in for confession and the old priest listened to her. When asked what sins she had committed, she said things like, I fornicated, and committed adultery! The whole time, the priest is saying, "do tell!" Of course, she committed non of those sins, she was just trying to connect words to her little sins like taking cake with out permission! It had me rolling, it was so funny!