Where can I listen to daily news reports in the language of my choice?

I want to get my ears accustomed to listening to certain languages that I’m interested in learning (or learning better), in the manner described in this New York Magazine article, for example — How to Learn a New Language Faster Without Paying Attention

So I was wondering if I could find daily, five- to 15-minute-long, international news summaries — say I want to listen to them in Bengali (a language I have some facility with), Italian (a language for which I know a handful of words and phrases), and Welsh (a language that I know almost nothing about).

Does anyone know of a convenient site where I can just turn on the news for each language while I’m doing something else?

Try BBC - Cymru for podcasts.

There are quits a few sources for finding live-streaming radio from every country in the world. One is Stream Radio By Location | Free Internet Radio | TuneIn but there are others you can find by googling.
Pick your country and search from the list of stations that live stream. It’s pretty hit and miss, because stations keep changing their links to live stream and the link is often outdated or dead. But a bit of perseverance, and you should be able to find a station broadcasting regular news broadcasts.

But once you get to the station’s site, it can be hard to identify the “listen” button, which will be in that language only.

Yeah, I was hoping for something much more convenient than that. I don’t really want to dig through a million sources to find something and also have to worry about its not being a credible mainstream news source. I was hoping I could just go to something like the BBC or Voice of America and click, click, click, line up 15 minutes worth of daily news summaries in three languages that would just automatically set up, like a podcast feed or something.