There are many ways to get wire coils, you can find lots of ideas online. Here's a summary:
1. Hand wind wire around a rod of the desired size - you can use metal rods, metal hole punches, plastic pen barrels, knitting needles etc. Wood dowels and skeweres don't work that well because tightly wound wire can crush the wood and get stuck on the dowel.
2. Hand wind wire on a crank style mandrel - this is easier on your wrists.
3. Insert rod into the check of a and electric screw driver or drill. Wear gloves to protect your hands and guide wire onto the slowly spinning mandrel. Use scrap lumber with a hole drilled in one end to support one (or both) ends of the mandrel as it spins. My son has strong hands and loves to use the cordless drill driver to wrap coils - I like to hand wind coils.