Each weekday (and occasionally on weekends), the Vatican publishes a news bulletin in Italian around noon Rome time. It is then translated into English, Spanish, Italian, and French, and posted online, as well as emailed out to a list of subscribers (usually by about 3pm Rome time, or 9am on the East Coast of the USA).
Included in each day’s bulletin are brief summaries of speeches and homilies the Holy Father gave, notices of which bishops and heads of state he had meetings with, news about major events happening in the Church, and news about newly-named bishops. To get a sense of what is included in it, you can scroll through past headlines on this page.
Why not get your Vatican news direct from the source? If you don’t already receive this daily news bulletin, you might sign up for it and give it a try. It’s a nice way to learn about what is happening in Rome and beyond.
Another site that I highly recommend for getting Church news is News.va.