I would be really carefull about that, I had 4 buttons in a pen and all got eaten buy 6 foot long rat snakes. Those guys can scale the hardest of walls and fit through the tightest of spaces. They are big and scary and I swear we made that pen bullet proof and he still got in. Best to put them inside.
I have my coturnix in a large rabbit hutch, in with two hen button quails outdoors. they have an indoor part to keep out of the elements and a tarp to keep out the drafts.
I plan to build the coturnix a tractor next spring/summer to let a few out to enjoy the grass and scratch (like they enjoy doing) in a few small pairs at a time fo ra few hours a day.
I will be separating the coturnix quail into trio breeding pens (they are just hanging wire pens) next spring/summer. <---these are simliar to Sportees picture above. The button quails will stay in the rabbit hutch.
I dont use nest boxes at all, as i dont think mine would use them, they lay whereever they want to.