Amplify coil antenna signal
If you are willing to calibrate each unit and then run it over a controlled temperature range, what you want should be doable.

The biggest issue is no the gain error, but maintaining good signal to noise ratio.

"Resonant capacitor" makes no sense, but resonance can be useful if the bandwidth of your signal is known and limited.  This is usually the case when receiving radio transmissions.

At 100 kHz you can amplify the signal directly without fancy stuff like mixing with a intermediate frequency, then amplifying that.  A LC resonant filter or two in the chain would be useful to reduce the gain at frequencies you don't care about.