32 awg Kanthal A is most popular -
coinswiesiek is a great ebay seller, but is out of stock. He has a hard time keeping it in. He has Nichrome 32 awg. Nichrome works, but doesn't have as high a heat index and burns out more frequently.
Ebay's pmtool appears to be out too. No luck on amazon either.
As to your question, Yes, 36 awg will work (the IAtty uses 36). Just remember that you'll need to measure the resistance on your coil so you don't overload your battery... some will take lower resistance, others need higher ohms.