Here is what I'd call a typical semi-tame canary
And here is something that says how to train (but you are on this forum - so you probably already know how to train)
Please don't use a tiny cage like you see in the first photo. Canaries need to fly in order to be healthy. You can do as small as 30X18X(18??) but a flight cage would be even better. Canaries have similar dietary requirements -- pellets, veggies, seed. They like a little fruit including oranges. Their seed is smaller than a conure's of course
They are a wee bit bossy, at least all my Glosters are. You wouldn't realize it because they look so sweet. One of mine was unhappy when she lived with canaries, then unhappy with the juvie canaries and juvie finches. Now she has moved herself into the cockatiel cage and she is happy as a clam!
There is not a problem with it being near a conure. I wouldn't start out with them loose together though -- either switch off out of cage time, or really REALLY supervise until you see what's going to happen. All of my birds (pionus, tiels, canaries, finches, and parrotlets) are able to fly around the room without bickering, it's a normal bedroom maybe 10X14. The notable exception is my caique who cannot behave herself and eventually nips someone.