Yes, you can train a canary to sit on your finger but it won’t happen straight away so be prepared to be patient throughout the entire process.
The first step of training your canary when you bring them home is letting them get used to their surroundings. Keep the cage at eye level so no objects or humans are enclosing them. Make sure the room is quiet but still has people quietly coming in and out so they can get used to humans being around them.
Then you’ll want to begin coming acquainted with your canary. Speak to them softly at eye level in the cage and always approach them slowly. Sit next to them for 15 minutes a day and you could even create a signature whistle that they’ll be able to recognize you by. You should always try to approach them when they’re relaxed on their perch and not around feeding times or if they’re fluttering around their cage.
The next step is to place your hand inside the cage slowly. Your canary might put up a fuss but try to ignore them and keep your hand still until they’ve calmed down and come accustomed to your hand being there. Then when your canary no longer makes a fuss, you can begin to introduce treats to them at your fingertips, they probably won’t take the bait straight away but be patient.
Depending on how confident your canary is, they may begin approaching your hand with the treats and may even end up sitting on your finger or perching on your hand.
They will soon associate your hand with food/treats so once your canary sits on your hand inside the cage even when you have no food, you begin to slowly retrieve your hand outside the cage with them sitting there. They may not be happy with being moved whilst perching on your hand, so begin with offering your hand near the cage door to start with.
For the next 4-6 weeks, slowly coax your hand outside the cage, make sure the room is sealed so they can’t fly off. Don’t react suddenly if they do fly off and let them make their way back to the cage themselves.
You can then begin training and luring her with treats to come land on your hand or a perch in the room after this point. Whenever she lands on your finger, reward her with a treat so she’ll be more likely to return.