I came up with the idea for the word "Psyrens" as a song title back in 1999/2000. After it ended up as the title of said song, I was curious to find out if it was original as a word so I searched the internet and, surprisingly found absolutely nothing at all!
Obviously this doesn't mean I was the first person to come up with the word and someone else probably did before that, just pre-internet.
Anyway, since 'Worlds...' came out the word has proliferated massively and is now used as peoples usernames, avatar names, characters etc, which is cool and might just be co-incidence. I guess that song got mentioned loads and loads in reviews of 'Worlds...' and thus the name spread. There's even bands named that now and the Manga (which I wasn't aware of until you pointed it out) which was only released in 2007.
So you won't find a definition online seeing as I made the word up for the song
Read the song explanation in the following page, which is about all I want to say publically about this song. You're quite close in your suggestion as you'll see.