How can I convince my mother to let me get a canary?

I am 14 and a huge animal lover. I spoil my pets and take care of them extra well, but my mom doesn't want any more pets. I promised I'll take care of it and I do lots of research before getting a pet. I've never had a bird, so this is what I want. Also, I'm not greedy. I'm not the girl who's constantly asking for clothes, jewelry, and I never ask for money because my friends and I don't even like to go out. I could care less about that stuff. I just love pets, they make me happiest. I have 5 pets currently. 2 cats, (but are 18 years old and who my mother has had for my older sister since before I was even born. And they are both sick and could sadly die any day now...), a shih-tzu (who's everyone's pet in the family, and we all care for her equally), a guinea pig (this one actually requires the most work and money), and a betta fish (who I care for 100%). And I either wanted to get two turtles or a bird, and I figured birds are cheaper and easier. (Plus turtles can live anywhere from 20-100 years!) I'm going to start doing better in school and help out a lot more. So how can I convince her I'm ready for another pet?