So your church doesn't have an app?

My church does not have a custom phone app. They're costly to commission. A church member with the right development tools can do it, but then there is the maintenance and dealing with the app stores.

However, my church uses a content management system (CMS) for its web site maintenance. The web site has a "what's new" section for time sensitive, newsy items. The CMS stores these sorts of items in an RSS file.

Try entering your church web address followed by an RSS feed name:
churchy.com/rss.xml
or maybe
churchy.com/feeds/

Once you know you have an RSS file, just tell your members to install a feeedreader app like Feedly. Suddenly, you have a little bit of a phone app!