They're more common than you probably think!
Check out the list view to see month and day records for each film here.
Dates used to compile this list are what come back from the TMDB API as its release date and appears to be the earliest theatrical or digital premier date. I am automatically excluding any films have a January 1st release date as that seems to generally be the default date in TMDB if there's no specific month or day. There might be some false positives getting filtered out because of this but it seems extremely unlikely.