Since you are using pallet wood I’m thinking you are going for a rustic look. I built a vanity and medicine cabinet for one of our bathrooms a little while back, and I used the top part of railroad spikes for the knobs this might work for one or more of your coat racks. The spikes are really cheap and easy to find (I got mine from a seller on Etsy. I just cut the tops off, drilled and tapped them, then mounted. Cabinet knobs and handless are pretty much a universal size, so you’ll need to buy a package or two of #6-32 screws, length depending on the thickness of your wood. You can get the screws from a home improvement center. You can also get your #6-32 tap there. You don’t need to buy a whole set, the stores sell them individually and the prices are reasonable. You could also use the ends of cutoff spoons, or anything else you can think of. I am including two pictures of the knobs on the vanity, and the medicine cabinet, but they came out grainy for some reason. Maybe because it’s nighttime.
Here are several styles for you to choose from. They're all pretty.
Thank you so much for responding. Much appreciated.
Make sure that you take the necessary precautions when using pallet wood. It is not designed for indoor use and may contain chemicals that can cause health issues.