It's good advice to get a larger coop, and if you want a quick, no-fuss, effective way to keep them safe from predators until you get a run built I'd recommend electric poultry netting. I wish I could figure out a way to get paid for endorsing them, but Premier 1 has great netting that you can buy in kit form with everything you need in one box: 100' of netting already on posts that just stick in the ground, the charger (solar/battery and AC), and beefier end posts. One person can set it up without a problem and it provides enough of a jolt to discourage dogs and even cattle. It would work as a run until you can build a more permanent one, and then it works well as a yard outside the run. Our barn/coop/run/yard are about 400' from the house, but with the electric netting up and hawk netting over that we're comfortable not having the birds constantly in view. The electric netting is easy to move around as they wear down the grass within it, although the company sells more permanent styles, too, and if you need to store it it rolls up into a nice tight bundle. We use the electrified netting even though the barn and the yard/run are contained within a 2-acre pasture fenced with goat fencing. For the peace of mind the $187 kit has been priceless. We used hawk netting above the yard and although it does prevent aerial predation it was a massive pain to install and I don't recommend that type. There are other stores online that sell netting that would be a lot easier to work with, like the kind used as baseball and golf backstops, and if you don't want that expense then the plastic deer netting for bushes would work really well, and it's super easy to work with. It cuts easily but it's hard to rip and it just has to be a visual barrier to hawks. It's easy to attach with staples, velcro, or zip ties (or a combo of the three) to just about anything and it's black, so it's less of an eyesore than hawk netting, which is made from white fishing line.
This isn't a great view, but you can see the posts for the netting outside the run with the white net stretched above it as a hawk barrier. Half the run is screened off with deer netting to separate the pullets from the hens.
A better view of the hawk netting over the yard, and you can also see the solar charger for the electric netting on a t-post at the left corner of the run. We used a heavy-duty tarp as a roof for the run because we couldn't afford any kind of solid roof. You can see the seam on the deer netting that divides the run in half: That's two strips of it zip-tied together lengthwise to make a barrier that even bluebells can't fly over. If you hung that stuff parallel to the ground it would work great as an aerial barrier.
Finally, I don't know if it would work in your application, but we had a bunch of spare metal bird spike strips that were a total failure at keeping swallows out of the eaves. We repurposed them as predator barriers around the base of the run on the outside, as an alternative to burying wire cloth. We just screwed the spike strips to the bottom 2 x 4s on the run, and good luck to any animal trying to burrow under them.