Try fresh fruits. Canned veggies are probably too salty, but frozen ones are fine. Check the internet for lists of things to NOT feed parrots (like avocado). Keep trying-it took the better part of a year to get Corsair

to try broccoli, but she happily munches it now.
As far as how small you cut things, it can depend on the bird. A lot of people dice things so the bird can't just pull out favorites. I'm usually too lazy for that, but cutting up berries can mean that Corsair doesn't have to hold them in her foot and track berry juice all over the cage. The first time she had strawberries everyone thought she was bleeding on her perch.

Remember those beaks chew through wood, so getting through peels, rinds, and skins is a matter of motivation-just let them know something really good is inside and they'll forage it right out (I'm thinking of tangerines right now-if anyone picks one up, Corsair demands her share)
Yams are good for most parrots-I microwave them until they are soft, then slice and chop for ease of eating. She likes them better with cinnamon sprinkled on them( Me, too!). Plain oatmeal and brown rice get cooked as if for me, but without salt. Cool before serving, and store in the refrigerator.
Carrots often need to be grated to get her to touch them-unless she changes her mind again!
Dried fruits are another favorite-raisins and cranberries mostly-but we save those for training treats because they add sugar to the dried cranberries(not something she needs), and if she tosses raisins outside the cage the dogs might get them and get sick. Other dried fruits don't attract her as much.
I hope this helps. It should get you started at any rate.