Quails (especially japanese quail, which is a quite small bird) are usually kept in greenhouses (at least in europe) in order to contral snails and slugs... I think they can also tolerate some low temps... Sometimes also some other small Phasianidae (e.g. Monals and Tragopans), but they are normally more expensive
They can do fine with concrete floor, just set a sand corner for them, and also a corner where they could hide.
For other birds, it would depend on the size of the greenhouse and the temperatures you have in it. Fruit and ground doves, trushes (e.g. white rumped shama), Mynas (can be very very loud!! go to Maui, and you will know what I mean with loud!!), Java Sparrows, Leiothrix and White-eye, are also commonly seen in warm (and also humid) greenhouses...
Conures and other parrots are lovely, but you should have at least two as tehy are very social birds... however, I would strongly not to keep them free in the greenhouse, as they will end up eating your plants