Do you know of trick training? It's fantastic for birds and once they get it down they LOVE it. The moment Rosie see's me getting the ready to train she is super excited, it's her favorite activity. My friend has taught her cockatiel to spin, wave, eagle wings, and say a few words when she queues him. My friends and I all use clickers to aid in training. Clickers really help the birds to understand what your asking them to do and make training much faster and less frustrating for the birds.
Clicker/trick training is wonderful because it not only is fun for your bird, but it makes them use that intelligent brain. They love using their brain and it makes happier birds.
Other than teaching tricks, I play with my birds by playing tug of war with a rawhide lace with a bead on one end. I drag it around, they pick it up, and we tug back & forth. I also take a small tea towel, and drop it over them, and lift it off, playing peek a boo. We play hide & seek the same way, gently chasing them around. Another game my 'tiel likes is find the seed. We play that with 3 tiny condiment cups from fast food places. I put my hand up, so she cannot see which cup I hide the seed in, then raise my hand, and she finds the seed. Games you can play with human babies are fun for your birds.