The first vegetable my guys tried (and loved) was sweet corn kernels sprinkled with a teeny bit of garlic powder (NOT salt).
Budgies seem to love "spicy" tastes.
My guys adore fresh basil, cilantro and chickweed.
They also like zucchini and red pepper.
The only veggies mine has been interested in are carrots, green pepper and red pepper. I cut them up into very tiny pieces which makes it easy for her to eat. She spends most of the day outside her cage so I place the veggies on a clean placemat in an area that she likes to hang out. Its pretty much trial and error....mine has had no interest in any kind of fruit.
Deborah has given you excellent advice and links to read through. Try offering the veg a different way, my guys love basil, thyme, parsley, carrot yams, fresh grass with seed heads. broccoli. don't give up .
Patience is the key, and presentation can make all the difference too. Lot's of good info Deborah has provided, and the thrill of seeing them eat veggies will be well worth your effort's not to mention the positive health impact on your bird...