The key to successful feeding of green food to your budgerigars is little and often. Lettuce and celery will be enjoyed by your budgerigars, but they provide very little nutritional value. For budgerigars in a birdroom or aviary they really enjoy corn-on-the-cob whole. In pet cages you can feed small amounts of apple and carrot.
Other green food such as chick weed, or groundsel will be readily eaten but you must ensure that it is free from any contamination.