I think OP is probably gone, but I wanted to comment on 41Gryphon's suggestions, which are good ones for someone who wants a cuddly bird bit isn't willing to commit to a parrot, and is willing to accept that such a bird won't be as interactive as most parrots are. I think that one of the reasons parrots are so popular is that they have the some of the highest reward for the investment among birds. Mousebirds, for example, are reportedly at least as affectionate as the similar-looking cockatiels, but require feedings of fresh fruit several times a day. And then you have hawks and falcons, which require a high time investment (a falconer told me it's about two hours a day for the first bird and an hour for each bird after that), which will never be that into you. With most parrots, the most demanding part of caring for them is socializing them, and if you
like birds, that doesn't seem like a chore.
I've met a few doves that liked to be cuddled, but I'm not sure if they were handraised.
I was able to handle
wild doves (doves, not pigeons) that I found nesting in a city Starbucks. It was after dark, and they were foraging on the balcony but couldn't really see very well, so one of them let me pick it up and put it on my shoulder, where it sat for about an hour while its mate stood watching in concern from the rail. I didn't actually cuddle it though because it was a wild animal possibly carrying zoonoses (I washed my hands when it finally fluttered off my shoulder to join its mate), but doves are certainly sweet animals, and though they're not as interactive as parrots, I've heard that they'll come to you if they recognize you.
Chickens and ducks aren't really well-suited for an apartment, but maybe look into quail? They're smaller and can be kept in a rabbit cage, but I don't know how friendly they can get.
Ducks generally aren't cuddly in my experience, though they're less vicious than geese. Hens and most roosters can be cuddled with impunity, though I've never seen one that seemed interested in people except as food providers, which I think is true of all fowl. They're precocial, and don't bond the way parrots or even doves do. I knew a Turkish guy who kept a partridge as a pet, and apparently they're moderately popular over there, but I don't think most apartments in the US would be OK with poultry of any sort. Your best bet for an apartment would probably be "buttonquail," which are typically seen as pets rather than livestock. The birds sold as buttonquail are actually true quail rather than buttonquail, so it's possible that other quail species also make decent pets.