Hmm.. I'm going to struggle with this one I think.
It's the words "write their vocals when the music is already finalized" that make it difficult for me. You see, I have never done that.
For me, the words and the music are partners, equal ingredients in a song. If anything, words are MORE important to me - but even they can't be finalized until the song is written. They (music and lyric) may need to adapt to work together.
Of course, it may be that someone else writes some music that is sacrosanct and the writer wants some words. I'm not sure if I could do that, but it would be interesting to try.
Part of me says that if the music IS the song and the words are really secondary, do they matter at all?
Maybe add some fashionable sounding but meaningless phrases to sound enigmatic and call the job done. Maybe the music is key (it probably is in some genres). After all, there was a hit in the UK way back called "Mouldy Old Dough". The lyrics were simply (you guessed it!) "mouldy old dough".. repeated. It worked.
However, it could be an interesting challenge. What is the song about? What is suggested by the music? Play it over and over to get an emotion from it.
Does a musical phrase stand out? If you repeat it over and over can some words come that just "fit"?
Write them down. Anything starting to spark? Be prepared to change them, but go with it. Write some more down. Hum over the song or phrase, burble out any old crap until something fits the feel.
You can do the "write down lots of 'cool' phrases on pieces of paper and shuffle them" trick.
Sooner or later, normally the song has to mean something by using lyrics that fit the musical feel. The vocal has to fit the music too.. it has to add something.. musically (see, I said it wasn't finalized
)
Sometimes it doesn't. Sometimes you don't need a lyric at all. Sometimes something very brief is enough
"Je t'aime" for example.
What style are you talking about? Want to put up the music? I bet plenty of people would give you at least a phrase, some of which may trigger something...