That will be high sensitive metal detector, so far I can detect cola can from 1.5m
For a low-power circuit you could use a varactor to fine-tune the capacitance, but for higher powers I'm not sure that's viable.
Highly stable LC circuits require the inductor to be rigidly mounted and kept at a fixed temperature to prevent expansion. Only high-stability dielectrics can be used for the capacitor, mica, PTFE and polystyrene come to mind. Also the capacitor needs to be sized for the current flow, otherwise it will self-heat too much - series/parallel combinations of several smaller caps will spread the load better.
Here the coil will be sensitive to nearby conductors and magnetic materials too, so care in positioning it is needed.
Any free-running LC oscillator is going to be less stable than quartz, but a well designed one can be pretty good.
The problem was in capacitor voltage, I used for 2000V, I know that I have high voltage but didnt expect more than 1500V, it turned out that is over 4000V.
Now LC is stable.
That is a high voltage 
Please let us know about the progress or the finished project.
A two-coil circuit is supposed to be more sensitive - one that uses coils arranged carefully to have their mutual inductance nulled out - objects in range detune this
null. This scheme is called an IB (induction balance) detector I believe.
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