Whether you don't sing regularly, or you're not singing at the moment, you'd still say it "Я не співаю", the exact meaning is determined by the context.
If you do need to be specific about that, you can add some words to clarify:
Я зараз не співаю - I'm not sining now
Я ніколи не співаю - I never sing
Я не співаю по понеділках - I don't sing on Mondays