SO we have some bubbles to burst here. Cuddling any parrot, regardless of species, is generally not a good idea. Our version of cuddling, to a human, involved touching, holding, scratching or otherwise contacting the parrot somewhere on his body. Those areas are considered inadvisable because they can trigger mating behavior. Humans cannot give a parrot who is in that hormonal mating condition the release they would get in nature by sex with a partner. Despite all the Youtube videos to the contrary, cuddling parrots is just creating an unnatural dynamic in the bird, which can lead to all sorts of releases you don't want, like biting, screaming or the worst - plucking, barbering or even self mutilation.
Secondly - there is not really a species that 100% of the members are going to universally like cuddling, it's very much an individual thing. However, there are several species that almost 100% of the time do NOT like cuddling or petting or scratching in general. Eclectus parrots and the whole ringneck family ( ringnecks, Alexandrine, plumheads and others in that family) have totally different feather structure then the rest of parrots and its pretty rare to find individuals who really enjoys a good scratch like Amazons, Cockatoos, Greys, and Macaws do. SO while you might find individuals who tolerate scratches within each of those species, the vast majority do not and a lot of them will deliver a nip ( or more) to indicate just how much they do not enjoy it. So if your going into parrot ownership, you have to keep that in mind and if cuddling is a main reason for selecting a parrot as a companion or pet, you really need to get to know the parrot well before you commit to getting that individual. Its the same like talking - some species are well known for talking great, like African Greys or Amazons, but there is no guarantee that any one individual is going to even talk at all. Some do and some never utter a word.
God on you for doing your research before comitting to ownership!