Whether or not a bird is able to be handled/petted or is cuddly/friendly doesn't have anything to do with the species of bird it is, but rather how they are raised by their breeder. The reason that most Budgies nowadays are not tame is because 95% or more of them that are sold are not hand-raised at all, but rather parent-raised and have little to n contact with people before they are sold, and this goes for not only the Budgies that are sold in pet shops like Petco and PetSmart, but also most Budgies that are bred and sold by private breeders. It's impossible to make a profit hand-raising Budgies, and the same goes anymore for Lovebirds, Cockatiels, etc. The profits in bird-breeding come from the species of parrots that you can sell hand-raised for at least $300 and up, which is why most of the sweet, loving, cuddly pet birds you see nowadays are the Conures, Quakers, Poicephalus, and any larger parrots.
I have 8 of the sweetest, most cuddly, most loving Budgies that you've ever seen, every bit as cuddly and able to be handled as my Green Cheek Conure or my Senegal Parrot...but that's because I bred them and hand-raised them myself from the time they were 2 weeks old..So this goes for all species of birds; if you go and look at parent-raised Green Cheek Conures, Sun Conures, Macaws, Greys, etc., they will not be able to be handled or petted either...
So the question that you should be asking yourself isn't "What species of small bird will be loving and cuddly and able to be handled?", as that applies to any and all of them...The question you need to be asking is "What species of small bird has the personality that will fit with me and my family? What species of small bird will have the energy level and needs that my home, my family, and my lifestyle will accommodate?"
Once you narrow it down to a specific species of small bird that you and your lifestyle and living situation are able to accommodate and that you think will be a great fit to add to your family, THEN you need to make the decision as to where to get the bird and what you want it to be like when it is brought home: #1) If you want it to be sweet, loving, cuddly, easily able to be handled, etc. right from the moment you bring it home, then you need to find a Hand-Raised baby of that particular species that is fully weaned and ready for it's new home, or #2) If you are willing to commit to hand-taming the bird yourself and are okay with bringing home a bird that is not able to be handled and that isn't cuddly and loving right from the get-go, meaning that you'll have to put in the time every single day to tame/train him, and are okay with the fact that it may very well take months or longer to accomplish this, then you can look for either a parent-raised baby or adult of this particular species, or you can look-into finding one at a bird-rescue and adopting...
If you decide that you want a hand-raised baby, your options, or at least your best option, is to search for a private breeder of that specific species online, and call around until you find one that has weaned or soon-to-be-weaned, hand-raised babies, and make arrangements to go and see them and interact with them. The other option for finding hand-raised babies of a specific species is from a pet shop who breeds and hand-raises their own birds IN-HOUSE, and this definitely rules-out Petco and PetSmart. Though Petco and Petsmart both sell hand-raised Cockatiels, Green Cheek Conures, Sun Conures, and Jenday Conures, they do come from "mass-breeding" situations, so sometimes they still require a bit of work to be able to be handled, and other times they are sweet and cuddly right off the bat...But as far as the Budgies that Petco, Petsmart, and most other pet shops sell, they are all mass-bred in huge warehouses and parent-raised, and typically they don't even interact with any humans until they are boxed-up and trucked to the pet shops...that's why you had such a hard time taming Budgies, as this process can take years to accomplish...
So the bottom-line is that you can find any species of small bird that you want that is cuddly and sweet and able to be handled right away, if that's what you want...What's more important is that you find the correct species of bird for you, your family, and your lifestyle first, then go from there....
