Hello. No, those two should not try to share a cage. They are very different birds in many ways. Different diets and different personalities being two of the most important differences. A Canary is not a hands on bird and will not be interested in coming out of the cage to spend time with you. The Parakeet is very much a hands on, "people" bird. They need different types and sizes of perches, toys, just about everything. I'll give you some links here where you can study up on proper diet for both of them and you will see it is quite different, even down to the seed mixes. But, very important, please notice that neither of them should be expected to live for long, or stay healthy, on seeds alone. The links will tell you about some of the consequences of the seed only diet such as the fatty tumors and fatty liver disease. I hope this answers the question for you but if not, or if you have more questions, just let me know. Patricia.
Click here: Hepatic Lipidosis
Click here: PetCareLibrary - Tumors in Parakeets (pvy.com) Click here: Parakeet Medical and Safety Information
Click here: Parakeet Budgie and Keet FAQs and Info Click here: Toxic and Safe Plants/Trees for Birds - Household Poisons
Click here: Birdsnways - Safe Plants & Trees for pet birds, pet parrots &exotic birds
Click here: Nutrition
Obesity & Diets (budgies)
Canary diet should be supplemented with hard-boiled chicken eggs, vegetable greens, calcium from cuttlebone, fruits, vegetables, and greens. You can also offer apples, oranges, bananas, green peppers, canned corn, fresh corn on the cob, cooked broccoli, carrots, raw spinach, raw dandelions, raw collard greens, raw Swiss chard, pears, peaches, strawberries, and cherries. The various berries are very good, especially for red factor birds. Iceberg type ettuce is useless and should not be fed. Cooked egg-white is also very beneficial for canaries, and most beneficial during molting.
Click here: All About Canaries & Keeping Canaries as Pet Birds
Click here: Pet Bird Canary FAQ
Click here: Feeding Canaries a Pellet Diet
Click here: The Pet Canary - Introduction and Care of Canaries