Since we know (in some traditions) monks and nuns can't work, what is meant by right livelihood for them?
Please check the following link. Right livelihood is explained in detail.
Right Livelihood for monks (in the Theravada tradition) would equate to following the dhamma-vinaya.
That is to work towards liberation for the benefit of all living beings and to act in accordance with this goal. The Buddha provided a set of 227 rules, which monks should abide by, for those who want to walk and live the path to its fullest extent.
Hopefully others can weigh in and quote exact passage from the cannon
I was reading and stumbled upon a sutra, which may add to the discussion.
“And what, monks, is right livelihood? There is the case where a disciple of the noble ones, having abandoned dishonest livelihood, keeps his life going with right livelihood. This, monks, is called right livelihood."