There certainly is a noun following 「~~ような」, if the noun does not directly follow it. That noun is 「[日課]{にっか}」.
「いつからか、[翡翠]{ひすい}がやってくれば[平穏]{へいおん}な[朝]{あさ}を[迎]{むか}えられるような、そんな日課が[出来上]{できあ}がっている。」
「翡翠がやってくれば平穏な朝を迎えられるような」 is an adjectival phrase that modifies 「日課」.
「そんな」 also modifies 「日課」.
「そんな」 here means "that sort of". The author could have just said 「翡翠がやってくれば平穏な朝を迎えられるような日課」 without using 「、そんな」.
「翡翠がやってくれば平穏な朝を迎えられるような」, however, is such a long and eloquent adjectival phrase that it could sound a little "affected" if the author placed 「日課」 directly following it.
By placing 「、そんな」(= "that sort of"), it could serve as a softener that brings the eloquence level down a bit.
My shot at a TL:
"Since who knows when, a sort of a daily routine has been formed in which I feel as if I could greet the dawn peacefully whenever Hisui comes/is here."