Understanding a coil I want to activate
My question is: Can I deduce for sure this is an AC coil requiring an
  input of 2.1 V and 31 mA?


No. Volts = Amps x Ohms. 0.177 A x 64 &ohm; = 11.38 V. The "OL" DC voltage reading means your meter was overloaded, perhaps because it was set to Ohms instead of Volts. The 2.1 V and 31 mA AC reading was probably ripple from the unregulated power supply.

My deduction is that the electromagnet is designed to operate from (approximately) 12 V DC.