Canaries are among the most beautiful, talented and yet private of all birds; they’re fine around their own kind for the most part, but tend to clam up and get shy among other species of birds. The finch, on the other hand is also a specimen to behold, with few talents and has a flare for being around other breeds of birds and also people. While canaries are a shy bird, it’s a known fact that if they can stand any bird, it’s the lovely finch — thus the canary finch connection.
The canary finch relationship depends on proper space, feeding (they love the same kinds of food), and the personalities of the individual birds you have. Another important fact of note, is that your canary will very likely stop to sing if it’s a singer. This should be of no concern though, as a canary will only sing if: A) It’s alone, or B) During molting season.
Your finch will absolutely love the company and will work very hard to break the ice with a canary, as it’s an animal/people pleasing bird. It’s best to keep them in separate cages if possible: It will be best for them to co-exist that way and then proceed to allow them to socialize through the cage — occasionally coming together during cage cleaning time while perching on a lamp-shade or counter-top.
As mentioned already: They can share the same food (although the finch can handle many seeds the canary will not) and feeding habits and will quite likely be able to stay in the same cage with one another. If you decide to try and bring the two together in the same cage, be sure to carefully observe them their first day together. In particular, watch the canary to see if they seem overly put off, or annoyed by the finch and you may make a canary finch connection in your own home.