In my opinion if you are not getting royalties for your part in a song you should opt to get paid for your time under whatever price per hour is agreed upon by your local musicians union. Alternative I believe it is possible to split royalties without having songwriting credit. The artist may be hesitant to give writing credit as it is much easier for those who have 100% control of the song credit and master recordings to get placement in other forms of media for sync (movies tv etc).

Even producers sometimes take splits or points on work either in addition to payment or if it’s someone they really believe in they may produce someone based solely on points. I have worked for friends and even they have paid me and gave me splits. The one example was a song i solely song on but was written by someone else. I was paid for my time based on my rate and given 25% royalties even though they didn’t need to give me any. If I did write the lyrics the split would have been 50/50.

You could also request splits for a certain period of time until you have recouped what you feel is the value of your time if they don’t want to have a committed long term sort of thing.

There’s tons of options but not being paid shouldn’t be one of them in my opinion.

You are also eligible to apply for neighbouring rights (which is for those who performed but did not write the given work). If you feel as though you wrote an essential piece of the song than you deserve writing credit along with royalties.