Is compatibility with cockatiels a requirement? Tiels are generally more mellow than a lot of other species and might get picked on or even hurt as a result. A parrotlet can easily intimidate a cockatiel even though it's smaller, and sometimes lovebirds will actually kill a cockatiel. Sometimes budgies get along with cockatiels and sometimes they don't - the budgie might beat up the cockatiel and vice versa. Many of the birds that are about the same size as a tiel (the smaller conures, senegals, etc) have much larger beaks, so if there was a fight the cockatiel would be at a big disadvantage.
Here's a suggestion for something unusual: a Princess of Wales parakeet. I don't know much about them and you'd need to do some research to find out if they're actually suitable, plus they're not all that common. I don't know how they feel about cuddling. But they're absolutely gorgeous, are slightly larger than a cockatiel with a relatively small beak, and have a reputation for gentleness. I was lusting after them at a bird mart today!
Here are some links about them:
Princess Parrots aka Princess of Wales: Species Information and Photos
Princess of Wales Parakeet, Ruffled Feathers Aviary, handfed baby birds For Sale, California, handraised Parrots, we ship (note the price tag of $200 for a handfed baby!)
