Disclaimer: I've never run phpBB myself or tested the following mods, and since web development is something I only dabble in, I'm not fit to authoritatively say whether they are safe/suitable.
There were several that I saw when searching for "RSS" on
the phpBB mod database. I think the most promising-looking one that I've seen (from the standpoint of documented features) is
Simple Syndication. Seems to have all the bells and whistles a user would need to tailor the feed he wants.