The 115 doesn't go to zero because it's actually measuring that resistance. You can try cleaning the contact surface of the leads. You can also go with gold plated leads. Fluke's standard leads are harder alloy for better wear but that means slightly higher surface contact resistance. Do you have other leads you can try or even just a bit of raw, multistrand wire jammed into the meter jacks. Bare wire should still show something like .1-.3 ohm.
Here's the other thing you can do. If you are concerned that there could be surface contact resistance, touch the meter probes to one terminal of the coil. Touch them next to each other but not actually touching. That way the resistance measurement includes the wire, probes, and terminal contact resistance. That will give you a good way to zero your reading.
Also, while you have said what a good coil reads, what does a bad coil read? Are we talking about 0.6, 6.0, 6k? If "good" basically shorted while bad is kohms I'm not sure this matters much.