Can zebra finches live together without breeding?

you could try removing anything that could be used as a nest, food cups, etc. And don't give them anything to trigger nest building, string, hay, etc. Maybe they will remain platonic :) If they do lay eggs and you don't want babies, get some fake eggs and toss the real ones, let the hen sit on the fake eggs till she gets tired of sitting, that will at least stop them breeding for a little while.