I have used in the past a vintage Meteor winding machine. It’s basically a lathe with a turn counter. For one off or low serie you can probably DIY something pretty easily.
In particular the OP probably doesn't want to buy a $1,000 automated coil winder to put wire onto a 50-cent bobbin. If it's a one-off or very small run for which the primary goal is to do it with the least expense, look for fishing-line winders or you can DIY it like I did when I needed to wind some ferrites, get some pillow block bearings and a car window handle off Aliexpress, screw them onto a base, attach whatever you're winding the wire onto between the bearings and wind away. You have to count the turns by hand but either it's a small number of turns and easy enough to count or it's a large number of turns and being off by one isn't a big deal. Total cost was about ten dollars.
It's a great thing to do while you're calling your mom... 127, 128, 129, yeah, 130, 131, 132, uh-huh, 133, 134, 135, no, I'm still listening, 136, 137, 138...