Well there are a bunch of veggies that bird like, the thing to remember is that every single bird is different, each is an individual, and what one bird likes, the next bird might not. So the key to finding out what your individual bird likes to eat (and how they like to eat it) is simply trying as many different veggies as you can, as well as cutting them into different sizes and shapes, as that often has a lot to do with whether a bird will eat a certain veggie or not.
Rules to follow always are no Avocado or Onion, as they are extremely toxic to birds. And always feed Fresh veggies to your bird, never canned, as canned veggies contain few vitamins or minerals, as they've been cooked-out of them, and they also usually contain a lot of sodium and preservatives, such as nitrates and nitrites. If you find that your bird like cooked veggies, the best way to prepare these is to buy fresh veggies and then lightly and quickly steam them, using only water.
As far as individual veggies go, the basic favorites are fresh Green Beans, Pea Pods, Bell Peppers of all colors, different varieties of Squash, Broccoli, Cauliflower, Carrots, and then the dark green, leafy greens, such as Collards, Mustard, Turnip, Dandelion, etc. Stay away from Iceberg Lettuce ad the like, as they are nothing but water and contain no nutritional value at all...My Senegal and my Green Cheek also love Eggplant and Okra. Brussel Sprouts are also something that they usually like.
Remember that some birds like them cut into small-bits, some like large pieces that they can hold in their feet and eat. It's all about finding what your bird likes.
****If you look in the "Food and Diet" forum here, you'll find a ton a really great recipes for "Chops" to try mixing up, and these are great because you can prepare large batches, put individual portions into baggies, and then freeze them, and then each night you can pull a baggie out of the freezer and put it into the fridge so that it's thawed-out for the next morning.