I may have misled you. the coating on the wire only needs to be removed where it will contact the battery terminals.
I'm a bit concerned about the 9V battery. The coil may become quite hot and cause a fire or burn someone.
Caution! Too much current can be dangerous! As electricity passes through a wire, some energy is lost as heat. The more current that flows through a wire, the more heat is generated. If you double the current passing through a wire, the heat generated will increase 4 times! If you triple the current passing through a wire, the heat generated will increase 9 times! Things can quickly become too hot to handle.
A D cell battery provides enough current to lift several paper clips or a small mass of iron filings
You may need to sand the wire contacting area before each use. Use a fine grade sandpaper.
When you wrap the wire around the nail, make certain that you wrap the wire all in one direction. Wrap neatly from one end to the other. More turns will increase the magnetic effect.
Soft iron is a good temporary magnet. A steel nail will retain a lot of its magnetism once the current in the coil is switched off.
The battery will drain fairly quickly (in a matter of several minutes)
Usually the big problem is getting and maintaining a good contact at the battery terminals