I'll add - do you have any other requirements from your future bird, such as a character? If no, I think that a Bourke is the most suitable - they chirp mostly when it's "half-dark" - in the early morning with the raising sun and in the evening while it gets dark. Sure, they may chirp something during day but it's mostly single chirps.
About mornings - as I wrote, they wake up so early but I don't think it should disturb your parents sleeping - at least here, we all can sleep despite their chirps in another room, including my dad who easily wakes up because of different noises. Budgies chirp in the morning as well, but their noise is louder.
Some males may sing various melodies, but their voice is friendly - honestly, when I heard my male singing for the first time, I couldn't stop listening to him
I asked about other requirements because Bourkes have totally different character from other parrots and some people don't want them because they are too calm. Also, it's not a great species for somebody who wants a cuddly bird - unlike most parrots, Bourkes find any kind of touching (even head preening!) as violating private space
(the only exception is made for breeding needs)