Popcorn time music version?

I remember a long time ago it was easy to find songs with gnutella clients (like LimeWire, which was a well-known one at the time).

Perhaps you might be thinking of something overly specific. At its core, Popcorn Time is nothing more than peer-to-peer file sharing (specifically BitTorrent, but that's a technical detail). So what you should be looking for is a more general-purpose peer-to-peer client accessing a network that's popular and that contains the kinds of things you're looking for. Some possibilities to consider include gtk-gnutella, WireShare, and Tribler.

http://thenextweb.com/apps/2015/10/13/popcorn-time-for-music-is-here/#gref

https://github.com/tchoulihan/torrenttunes-client