My budgie seemed to take forever to try veggies. At first I tried chopping up carrots and other veggies but he wouldn't touch them. Then I tried clipping small peices of kale in his cage near a favorite perch. Eventually curiosity got the better of him and he nibbled the kale; then it didn't take long for him to try other green leafy things like lettuce (now he wont eat kale but he loves lettuce..) He's tame so when I introduced other veggies I would eat them with him watching, and he usually can't resist trying something I put in my mouth, so in that way I've got him to like carrot and ocasianally other veggies. If your budgies aren't tame it still might work to eat new foods with them watching; when you don't die they think "well it must not be poisonous and it must be food"...
Also, just choose a one food item in one shape/size and offer it every day and eventually they'll probably get interested and nibble it. My budgie tends to like green leafy things more than other veggies and ive read about other budgies having similar tastes. It probably has something to do with the fact that wild budgies eat grass seeds and sometimes they also eat the grass plants; they never really eat veggies or fruits in the wild.
Putting peices of vegetables in the food bowl might also work...
Good luck and be patient!