You can get polystyrene caps designed to be used in the local osc section of old tranny radios, these tend to be really stable, maybe not so much at 8kc though.
A silver mica cap might be better as you can get them in higher values more suited to lower freq's like 8 kc, they are reasonably expensive.
I agree with cruts, even an air core inductor will vary with temp, a ferrite core even more so.
By far the most stable would be a xtal divided down, but you dont want that, if you really want an lc circuit you'd probably have to use a ferrite core coil to get high enough inductance for that freq, try and get an old timer tube radio local oscillator transformer can and rewind it for 8kc, you'll need a lot more turns to get that frequency its a 100 times lower, you'll also need a high value resistor to get the current slope slow enough, but that might be possible with a cmos chip.