The easier way to talk about fruits is to talk about the dangers. In general, any fruit you can eat, your parakeet can eat too. You want it to be *fresh* - parakeet eyes are keenly tuned to seeing "less than fresh food". You would imagine this would be useful to them in the wild
So a food item that you thought was "so so" (like wilted lettuce) your parakeet would see as "really nasty"
So with that in mind, anything you would eat, cut fresh pieces into small cubes and offer that to your keet. Make it fun! Sometimes given them orange things, sometimes green things. Keets like new things to play with. Don't be discouraged if they don't eat something the first time - or fifth time. Sometimes it takes them a while to get used to a new food. Eat it yourself in front of them, show them it is yummy. That helps them learn it is tasty. Keets are very social animals and if you have something good - they want some too!
The only fruit-type to be concerned about are avocados, apple seeds and cherry seeds. Those are toxic and should be avoided.