Honestly, if you are FOSTERING a Sun Conure I would explain to her that yes, the bird will be loud, but it will not be permanent and you are doing something nice for an animal that needs help and special attention until she finds a home... and you're doing it out of your own pocket.
Ultimately though, it is your parent's house. Even if you are the sole care-taker, your mother might not appreciate the noise level of a Sun Conure in her home (I have a Blue and Gold Macaw and while she is loud, a Sun Conure... especially a rescued one... has the potential to be constantly loud. EEK EEK ECK ECK ECK EEK EEK ECK EEK. Personally I'd take my Macaw's evening flock call over that)
If it were me trying to convince my mother that I wanted another bird (especially considering she is not a bird person) I would try to go for another quieter type of bird. Chico is of the quieter types of Conures (from my experience). Perhaps go with a Quaker (which have a quieter chatter level) or another type of Green Cheek Conure or something.
I would worry that even in the short time you would foster that bird, your mom would hear the noise and be so offput by it that she would vehemently refuse to let you buy a second bird because she'd worry it would be as loud as the Sunny.
But, my advice may not be worth much, as I am 27 and own my own home in the country. I also hope this isn't too discouraging!... or too long of a message! I am pretty long winded, lol!