Yiddish, like other languages, has its own unique ways of expressing similar concepts. If you're looking for a Yiddish equivalent, you'd need to describe the specific facial expression or behavior you have in mind.
For example, you could say:
* "A shpielt a tzeik" (meaning "he's playing a role" or "he's putting on a show") to describe someone acting pious.
* "Er hot a kishkes in a kup" (meaning "he has a bellyache in his head") to describe someone looking miserable or unhappy.
* "A geit mit a shtrengel" (meaning "he's walking with a straight face") to describe someone looking serious or unsmiling.
Ultimately, the best way to express "church face" in Yiddish would depend on the specific context and the meaning you want to convey.